Please no. I'm a big fan of Avery, but he's also one player who can let things go up in his head. You'll have to worry of him beginning to try to do stuff that are beyond his skills just because he's "The Man" now.
Let him be were he is right now. No need to call him a Captain.
From a leadership standpoint, I have no problem with him being a Captain, but I would really worry about his floor play would be affected by it, and I don't think it'll be in a good way.