I wouldn't recommend doing it on soaking wet hair, just to avoid manipulating it too much while it's wet. Also, the waves of the braid-out would presumably be tighter if you did it while it was wet.
I used to dry in ponytails, with the hair in braids (to keep it detangled). When it got about 70% dry, I the ponytails out, added a little creamy moisturizer, chi silk infusion, and sealed with oil. Then I rebraided in whatever style I was gonna wear it (like, making the part, etc). I have fine, over-permed end, so for me, I find it best to take out that last set of braids before my hair is totally dry. That way, the ends can kinda fluff back up to match the roots.
Obligatory reminder about ponytail drying: They can cause breakage, just like ponytails, with overuse.
HHStyling!
eta: pics of braidouts
(the result of two cornrows on soaking wet hair in Aug)
(the result of a 4-6 braids on damp hair, probably day 2, in November)