You can turn off avatars in posts in Admin->Edit Theme-> Show user's profile pictures in their post. You also have the option to disallow the option of avatars. " Allow users to add a picture to their profile"
Individual users can change how this shows up for them by going to:
My Home->Display preferences, number of shown threads, languages, colors...->
View user's pictures with their posts?
Also has the ability to turn of avatars when view someones profile->" View other user's pictures in their profile?"
This is built in functionality on my 6.3.1 board.
ETA: I see this same functionality in the "Display preferences, number of shown threads, languages, colors..." of the My Home section of the 6.4 boards they are running here.