No, my avatar does not affect how I post. But it does reflect how I feel at the time I posted that avatar, so in an indirect way I could say yes. But really it's more of a reflection of me at a moment in time. I think that's the case for a lot of people--especially those of us the change our avatars a lot.
As for other people, yes it does at first. If I don't really know them well (by their posts) then I have to go with the available information which includes their avatar. After I get to know them though, the answer would be no. I then go by past posts and the picture of them that I've built up in my mind.