No. To tell you the truth, I rarely even bother noting what the person's name is, much less taking the time to look at their avatar. If something is posted that I should respond to, I just hit quote. The closest I come to looking at the person's name if I feel the need to respond to their post incrementally and will cut out the quote header so I can paste it in later as needed. Even then I don't really stop and read what it said.
Besides, so many of you guys have Avatars that, after a brief glance, tells me nothing about you as a poster. Take for example the countless avatars of some anime character or another. As a person who doesn't follow that particular animation style, you might as well just have the same avatar because all I see is random animated person. I get no context. The only thing I learn is that you probably like anime.
In some cases the avatar is at least distinctive, but that only helps you if you post a LOT (and thus catch my eye regularly), but even then having anything that catches my eye will help me identify you after time. As far as my posts are concerned, I am generally responding to a block of text that I may or may not disagree with. Unless you have done something exceptional to draw my attention, I will not attach any particular person or identity to your post. As such, I can safely say that your choice of avatar or name will only in the rarest of cases be recognizable, and even when it is it won't change what I'm going to say.