I rough turn all my work, NE or not, and return them after dried. I just find everything works better that way, for me at least.
There are MANY different ways and opinions about drying techniques and the same about turning to final thickness and letting them warp.
I prefer the 'roughing em out and let em dry' way.
Like Bill indicated, wet wood will not sand as well as dried wood without some sort of stiffening.
If you do rough turn it, leave it a little thicker, to account for warping. I think the standard formula is 10% - 15% of final diameter. So a 10" diameter bowl should be left about 1" thick. I don't hold too much to formulas and tend to go with what feels right. But its a good guideline.
Try a couple of different ways and eventually you will settle on what will become your technique!

Makes sure to secure your bark if you want it on. Either superglue it on or flood it with a stiffening finish, oil won't work. If you don't secure the bark it may warp off or fly off when you finish turning it.