Not without adding having the avatar to the list of available conditions, and that involves an addon.
I believe it's a fairly simple thing to do, and @Chris D created the addon for us, but time restrictions prevented it from getting released to the public in the resource manager.
I would be surprised if this wasn't a feature in the core of XF2.
This tutorial goes through creating the addon to check if a user has an avatar. I believe if you've no desire to learn that you can just download the file and install it anyway.
It does use template hooks which I believe are still valid but deprecated so it may need updating to the TMS system at some point.