With the tank being pretty well geared you should be fine, he will just take more of a beating due to slower kills.
Only fights that will be an issue is ones where there is a lot of AoE damage that your healer would need to work hard at. Overall I think you should be able to run heroics, although with the expansion on the horizon I would think of it as a learning experience rather than gearing up for the sake of gear due to it all being wiped with the expansion.
A bear tank can use quite a few PvP items due to their gear being a lot more stamina oriented, due to being automatically being crit immune..