You should read Jesse Martin's book "Lionheart"
-- he did a non-stop solo circumnavigation on an S&S 34 (at the time the youngest to do it).
Robin Knox Johnston's boat Suhaili
was 32' (he was the first to do it).
Of course, more telling than length would be displacement.
FWIW, you don't need to carry a year's worth of fresh water with you from the beginning -- you can make fresh water along the way (if you have enough fuel), or more realistically capture rainfall to refill your supplies.
Maybe not non-stop circumnavigations, but there have been a lot of other very impressive voyages in even smaller boats (e.g. "My Old Man and the Sea"
by David and Daniel Hays).
edit: another book to read -"Tinkerbelle" by Robert N. Manry
So yeah, I think it could be in the realm of possibility. Obviously it would require a lot of thought and careful planning.
If you get serious about something like this, you should definitely talk to Bruce Schwab
and others who've done it, like Tony Gooch