Personally for me while the avatar doesn't make that much of a difference, I can really see it doing a difference at the same time. If you use a avatar with someone sleeping for example I will definitively see you as a little bit more relaxed, even tough I don't intend to.
When I first joined the forums I thought it was kind of weird that the owner didn't have a avatar, but as time passed by I kind of understood why.
EDIT: Wait a little, Hey Remi that Remi bot, isn't it kind of representing you? If so why did you give it a avatar?
