Are you talking about a wrap? Well when I used to straighten, I'd sometimes wrap my hair as you described before I go to bed at night. I know some do it with wet hair, But I never did because my hair has always been to thick and long to do it wet. (even if I sit under a hair dryer, it still wouldn't dry.) anyway I always loved the results. I haven't tried it since wearing my hair curly. I doubt it would work now.
As far as a wet bun being good for the hair... I don't know. I do it a lot but that's because I don't have time to dry it before hand. I do know that if you choose to do that, don't pull too tight on your wet hair because that could cause breakage. And if you secure it with a ponytail holder, use one that doesn't have the metal clasp- Goody makes nice ones.