Probably not, it would make more sense if you don't see what characters they pick until everyone is locked in.
I love superpiposarus idea of a lobby though
I'm for and against the idea of seeing what your opponents pick.
BUT I would actually like to know, since I don't want to pick the same character as someone else.
Just because of the "I can't find my character" issue. I don't really have it, but generally I would love for 4 different characters fighting and I would gladly be the one moving away from my "main", if someone else picks her.
But again this would lead to counterpicking, even though all characters should be balanced enough against eachother.