For what it is worth, it does not seem that there is a universal vBcode or replacement variable for a user's avatar as of this writing. I did however write a complete hack that allows this to work with either custom or pre-defined avatars and it works flawlessly.
Unfortunately vBulletin.org is not allowing vb3 hacks at this time, so we're pretty much screwed as far as me sharing it with anyone.
I did post a question on vBulletin.com to see if the devs have hidden a globally accessible vBcode or replacement variable that we can call instead, but no replies yet.