I let it drain -- I don't, say, rack into a fermenter with a puddle of iodophor in the bottom -- but I try to use stuff while still "wet" as I figure that means it is still sanitized, as you say, narcout. Even though it's "no rinse," I like a balance between adding as little solution as possible to my beer and waiting so long that I might need to sanitize again. But...
On the other hand, maybe in an irrational contradiction, I often sanitize my fermenter ahead of brewing and close it up still wet. Does this carry a risk of something present on a speck of dust in the air inside contaminating my beer? I figure the wort will be in contact with the air as the fermenter is filled no matter what. Maybe should consider that with regard to saniting all equipment, so if it dries, the surface is only as prone to contamination from the the air as the wort itself is. If a surface has been thoroughly cleaned and sanitized once, maybe we shouldn't worry too much.
Here's my general philosophy. Cleaning is of primary importance, sanitizing is just feel-good insurance. Sanitizing is killing the stuff you left on a surface, cleaning is removing it in the first place. Clean surfaces are the least possible source of infection. The one thing we can't clean or sanitize is the air (unless you're brewing in a NASA clean room.)