Documentation requirements can be found in many threads here on sailnet, you can find them by putting "USCG documentation" in the search window and hitting go, or you can research the source here:
2001 CFR Title 45, Volume 4
The unasked question is, if you boat is not currently documented, then is it registered?
It must be one or the other even without mechanical propulsion. By the way, my reading of the regulations is it doesn't matter if the boat has working engines, it will still be considered a boat with mechanical propulsion.
Documenting a boat is cheap and easy, renewal is free. It literally serves no purpose at all to delay until you re-float it.