For example, my Sorcerer is decked out in a complete War Hero Force-Master's set. I've also augmented this with drops and purchases and participating in the game events. Will that armour set be worth anything in an operation?
Your WH gear is the equivalent to 58 gear in pve. Keep in mind that the stat distribution is a bit lower then pure pve gear. The armouring by itself is 30 points main stat lower. But I see no reason why you would be turned down other then people saying you shouldn't bring PvP gear to pve. But keep in mind these people have a sour taste in their mouths because pvpers get mad at them for showing up in a wz with all pve gear.