You can do it with default designs (I've copied the cargo carrier template into the large section), so I would assume you can with custom ships. The blueprint XML is able to assign a hull size to a template that was designed in another hull size.

I haven't tried with custom designs, but you should be able to do it if you mess with the ShipClassDefs XML. If you are using a custom ShipClassDefs XML you should just need to tell it to call a blueprint of the hullsize you want (eg, for medium change Blueprintdef to FrigateBlueprint).

If you don't have a custom shipset you'll have to mess with the core XML (always backup the XML files if you are going to mess with them). There you'd want to to change ShipDesign to point to the custom design. So if you are using the Terran shipset and want a medium hull, you can do to by going to TerranFrigate and changing ShipDesign from Terran_Frigate_02T to whatever the file name of the custom ship is.

Once back in the game and you have the hulls unlocked you should see your custom designs being used by the auto-designer. Though note with the second way the thumbnail will not match the design, it will show the core design, but when you select it the design in the main window should be that of the custom design. This doesn't matter, what you do next replaces it. Simply click "Use Design" on the ship and then tick "Save as Template", change the name and desc if you want and save it. This should now give you a template of the design in that hull size.

Once again, I haven't actually tried this, but given how the system works I'm fairly sure that it should work. If it doesn't say so and I'll have another look at it. Or maybe someone else will come by and will know of a different way to do it.

Thanks I'll try in in a few days and reply here so others can find out if it works.