I don't see why you couldn't do all of the level 70 instances with this setup if you swap into bear or are tight with heals. But it isn't going to be easy. Heroics? Heh. I managed to do all of the instances with a priest "tank" but I had tons of DPS and I was ultra fast on heals.

There are very few setups that are completely unviable, and I am not saying yours is but you certainly picked a strange combination!