It depends on the mod and how the things it alters are shared between host and client. Some mods like weapon velocities may cause weirdness for the clients that don't have it (projectile shuttering). I think the no tonnage limit one works since it is all host side. Things like UI tweaks should work fine.

Anything with new assets like mechs/weapons will either crash the client without it, or won't show up, etc. Not that those mods are currently functional.