Is it possible to add extra bones to something that's going to be used as a garment? I'm talking about adding bones to like a piece of the garment like the tails of a tuxedo or a sash because you want to make specific movements with it?

No, bones are stripped when skin weights transferred to cloth. Only morphs and cloth physics is supported.

Bones could be added to cloth on Humanoids though.

That coat on Humanoid girl had 9 bones. I through them into spring (no collision though - it's either-or).