Priests are heavily dependant on pvp gear. Now in a pve way, no. A Shadow priest can do extremely well with healing gear.
Priests more so than other classes. We also have the dumbest most confusing reforging priorities and there is never one clear cut option so that also makes gearing feel like even with gear you do no damage.
I can't speak for pvp, but in pve I think we are fairly dependent on gear. I only did good dps in healing gear (on accident) in 5-mans. In raids its another story. Sure we can get hit cap fairly easily, but without reaching the soft haste cap or have 2 piece are dps is so-so compared to other classes.