It makes it really weird when a bunch of Andraste-worshipping humies think you're divine. But a lot of people definitely acknowledge it at least in passing, if not in plot (i.e. you're not actually prevented from doing anything by being qunari, you can still get 100 approval at the Winter Palace, etc.). But you do get called oxman at least a couple times. You're also much taller than everyone else and look pretty impressive in cutscenes.
TIB convos have a lot of nice extra touches and lines too.
Bear in mind that you play a Tal'Vashoth(sp) rather than a follower of the Qun, so you can't go around enlightening people as to the proper philosophy or anything, but you can play a hardcore Qun wannabe mostly thanks to TIB's convos.
You will spend a lot of time in chicken armor (armor of the dragon) unless you gather a lot of mats and schematics, and the face paints can be quite horrifying, like, in a bad way.