you just have to add _C to the end of PrimalItemArmor_ClothShirt

Yes, that's with the default vanilla items. But I'm asking if there's a way to do it with mod items too, like items from this mod. Would adding _C to the end of the dragon saddle blueprint make it appear in the beacons as loot the same as any vanilla item, even though it doesn't specify to look into the mods folder rather than the default file tree?

Yes mod items can be entered, so in the case of wanting what tier level here is an example of what the code should look like:
ConfigOverrideSupplyCrateItems=(SupplyCrateClassString="SupplyCrate_Level35_C",MinItemSets=4,MaxItemSets=4,NumItemSetsPower=1.0,bSetsRandomWithoutReplacement=true,ItemSets=((MinNumItems=1,MaxNumItems=1,NumItemsPower=1.0,SetWeight=1.0,bItemsRandomWithoutReplacement=true,ItemEntries=((EntryWeight=1.0,ItemClassStrings=("PrimalItemResource_Metal_C","PrimalItemResource_Fibers_C","PrimalItemResource_Flint_C","PrimalItemResource_Chitin_C","PrimalItemResource_Pelt_C"),ItemsWeights=(0.225,0.225,0.235,0.225,0.100),MinQuantity=50.0,MaxQuantity=50.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=false,ChanceToBeBlueprintOverride=0.0))),(MinNumItems=1,MaxNumItems=1,NumItemsPower=1.0,SetWeight=1.0,bItemsRandomWithoutReplacement=true,ItemEntries=((EntryWeight=0.75,ItemClassStrings=("PrimalItemStructure_StoneTrapdoor_C","PrimalItemStructure_StoneWindow_C","PrimalItemStructure_MetalFloor_C","PrimalItemStructure_MetalWall_C","PrimalItemStructure_MetalWall_Sloped_Left_C","PrimalItemStructure_MetalWall_Sloped_Right_C","PrimalItemStructure_MetalWallWithDoor_C","PrimalItemStructure_MetalRoof_C","PrimalItemStructure_MetalRailing_C","PrimalItemStructure_MetalPillar_C","PrimalItemStructure_MetalCeiling_C","PrimalItemStructure_MetalDoor_C","PrimalItemStructure_MetalRamp_C"),ItemsWeights=(1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0),MinQuantity=4.0,MaxQuantity=6.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=false,ChanceToBeBlueprintOverride=0.0),(EntryWeight=0.25,ItemClassStrings=("PrimalItemStructure_StoneGateframe_Large_C","PrimalItemStructure_StoneGateLarge_C","PrimalItemStructure_StoneTrapdoor_C","PrimalItemStructure_StoneWindow_C","PrimalItemStructure_MetalFloor_C","PrimalItemStructure_MetalWall_C","PrimalItemStructure_MetalWall_Sloped_Left_C","PrimalItemStructure_MetalWall_Sloped_Right_C","PrimalItemStructure_MetalWallWithDoor_C","PrimalItemStructure_MetalRailing_C","PrimalItemStructure_MetalPillar_C","PrimalItemStructure_MetalCeiling_C","PrimalItemStructure_MetalRoof_C","PrimalItemStructure_MetalDoor_C","PrimalItemStructure_MetalRamp_C","PrimalItemStructure_Cannon_C","PrimalItemStructure_TurretCatapult_C"),ItemsWeights=(1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0),MinQuantity=1.0,MaxQuantity=1.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=true,ChanceToBeBlueprintOverride=0.0))),(MinNumItems=1,MaxNumItems=1,NumItemsPower=1.0,SetWeight=1.0,bItemsRandomWithoutReplacement=true,ItemEntries=((EntryWeight=1.0,ItemClassStrings=("PrimalItem_WeaponGun_C","PrimalItem_WeaponSickle_C","PrimalItemArmor_StegoSaddle_C","PrimalItemArmor_DoedSaddle_C","PrimalItemArmor_Paracer_Saddle_C","PrimalItemArmor_StagSaddle_C","PrimalItem_WeaponSword_C","PrimalItem_WeaponOneShotRifle_C","PrimalItemArmor_PteroSaddle_C","PrimalItemArmor_SarcoSaddle_C","PrimalItemArmor_DireBearSaddle_C","PrimalItem_WeaponShotgun_C","PrimalItemArmor_DiplodocusSaddle_C","PrimalItemArmor_ChitinPants_C","PrimalItemArmor_ChitinHelmet_C","PrimalItemArmor_ChitinShirt_C","PrimalItemArmor_MetalShield_C","PrimalItemArmor_ChitinGloves_C","PrimalItemArmor_ChitinBoots_C","PrimalItemArmor_GhillieShirt_C","PrimalItemArmor_GhilliePants_C","PrimalItemArmor_GhillieHelmet_C"),ItemsWeights=(1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0),MinQuantity=1.0,MaxQuantity=1.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=false,ChanceToBeBlueprintOverride=0.1))),),(MinNumItems=1,MaxNumItems=1,NumItemsPower=1.0,SetWeight=1.0,bItemsRandomWithoutReplacement=true,ItemEntries=((EntryWeight=1.0,ItemClassStrings=("PrimalItemStructure_Fireplace_C","PrimalItemStructure_CropPlot_Large_C","PrimalItemStructure_BeerBarrel_C"),ItemsWeights=(0.15,0.70,0.15),MinQuantity=1.0,MaxQuantity=1.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=false,ChanceToBeBlueprintOverride=0.50)))))
ConfigOverrideSupplyCrateItems=(SupplyCrateClassString="SupplyCrate_Level35_Double_C",MinItemSets=4,MaxItemSets=4,NumItemSetsPower=1.0,bSetsRandomWithoutReplacement=true,ItemSets=((MinNumItems=1,MaxNumItems=1,NumItemsPower=1.0,SetWeight=1.0,bItemsRandomWithoutReplacement=true,ItemEntries=((EntryWeight=1.0,ItemClassStrings=("PrimalItemAmmo_SimpleBullet_C","PrimalItem_WeaponGrenade_C","PrimalItemConsumableMiracleGro_C","PrimalItemAmmo_CannonBall_C","PrimalItem_PoisonGrenade_C","PrimalItemConsumable_Fertilizer_Compost_C","PrimalItemAmmo_SimpleRifleBullet_C","PrimalItemAmmo_SimpleShotgunBullet_C"),ItemsWeights=(0.05,0.05,0.05,0.05,0.05,0.65,0.05,0.05),MinQuantity=5.0,MaxQuantity=5.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=false,ChanceToBeBlueprintOverride=0.0))),(MinNumItems=1,MaxNumItems=1,NumItemsPower=1.0,SetWeight=1.0,bItemsRandomWithoutReplacement=true,ItemEntries=((EntryWeight=0.75,ItemClassStrings=("PrimalItemStructure_MetalPillar_C","PrimalItemStructure_MetalCeiling_C","PrimalItemStructure_MetalRoof_C","PrimalItemStructure_MetalDoor_C","PrimalItemStructure_MetalRamp_C","PrimalItemStructure_MetalPipeIntake_C","PrimalItemStructure_MetalPipeStraight_C","PrimalItemStructure_MetalCeilingWithTrapdoor_C","PrimalItemStructure_MetalTrapdoor_C","PrimalItemStructure_MetalFenceFoundation_C",),ItemsWeights=(1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0),MinQuantity=4.0,MaxQuantity=6.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=false,ChanceToBeBlueprintOverride=0.0),(EntryWeight=0.25,ItemClassStrings=("PrimalItemStructure_MetalPillar_C","PrimalItemStructure_MetalCeiling_C","PrimalItemStructure_MetalRoof_C","PrimalItemStructure_MetalDoor_C","PrimalItemStructure_MetalRamp_C","PrimalItemStructure_MetalPipeIntake_C","PrimalItemStructure_MetalPipeStraight_C","PrimalItemStructure_MetalCeilingWithTrapdoor_C","PrimalItemStructure_MetalTrapdoor_C","PrimalItemStructure_MetalFenceFoundation_C","PrimalItemStructure_MetalGateframe_C","PrimalItemStructure_MetalGate_C","PrimalItemStructure_Fabricator_C","PrimalItemStructure_Cannon_C"),ItemsWeights=(1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0),MinQuantity=1.0,MaxQuantity=1.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=true,ChanceToBeBlueprintOverride=0.0))),(MinNumItems=1,MaxNumItems=1,NumItemsPower=1.0,SetWeight=1.0,bItemsRandomWithoutReplacement=true,ItemEntries=((EntryWeight=1.0,ItemClassStrings=("PrimalItemArmor_PteroSaddle_C","PrimalItemArmor_SarcoSaddle_C","PrimalItemArmor_DireBearSaddle_C","PrimalItem_WeaponShotgun_C","PrimalItemArmor_DiplodocusSaddle_C","PrimalItemArmor_AnkyloSaddle_C","PrimalItemArmor_SpiderSaddle_C","PrimalItemArmor_MammothSaddle_C","PrimalItemArmor_DunkleosteusSaddle_C","PrimalItemArmor_ChitinGloves_C","PrimalItemArmor_ChitinBoots_C","PrimalItemArmor_GhillieShirt_C","PrimalItemArmor_GhilliePants_C","PrimalItemArmor_GhillieHelmet_C","PrimalItemArmor_GhillieBoots_C","PrimalItemArmor_GhillieGloves_C"),ItemsWeights=(1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0),MinQuantity=1.0,MaxQuantity=1.0,MinQuality=1.75,MaxQuality=2.25,bForceBlueprint=false,ChanceToBeBlueprintOverride=0.1))),(MinNumItems=1,MaxNumItems=1,NumItemsPower=1.0,SetWeight=1.0,bItemsRandomWithoutReplacement=true,ItemEntries=((EntryWeight=1.0,ItemClassStrings=("PrimalItemStructure_CropPlot_Large_C","PrimalItemStructure_BeerBarrel_C","PrimalItemWeaponAttachment_Silencer"),ItemsWeights=(0.70,0.15,0.15),MinQuantity=1.0,MaxQuantity=1.0,MinQuality=1.0,MaxQuality=1.0,bForceBlueprint=false,ChanceToBeBlueprintOverride=0.50)))))

The above is for a level 35 crate. Just make sure whatever item you swap out is swapped through the entire string.

Thank you for your reply. Hmm, that's interesting...I asked this question on another mod board as well, and the developer of that mod said that currently Ark does not support adding mod items to beacons, and that there was no way to make such a thing work. He said that the devs planned to make it possible in the future, but currently it wasn't an option.

I guess I'll have to run a test to figure out once and for all if it does work. Remove my current beacon script and replace it exclusivley with dragon saddles and helmets, see if anything appears in the beacons. I'll try it when I can, and if anyone wants me to post the results here then I will do so.

Thanks again for all the feedback on this question :)