Snake eyes can for sure do a stand 720, but I've only ever seen him take ultra one vs a few characters(Rufus). I'm pretty sure(completely sure) that it's buffered because it's safer AND easier(not to mention you can manipulate the range it hits at by whiffing. It's definitely not that he can't do them, it's just that the setups in which ultra one is relevant allows for it to be done in a pretty foolproof way.
Gief has 6 frame startup on his jump so as long as you can twirl it in 6 frames you can do it. Not to mention you don't need to do a full 720, just making it 7/8 of the way on the second twirl will work(pretty sure that doesn't work with Hugo though).