yes. anytime you add power symbols to a unit it contributes to which ever zone they're in. So if you're new to the game it can be easy to accidentally start drawing too many cards from those special powers.
You need to be careful what you play in your Questing Zone.
Though the same thing applies for the kingdom zone. You can end up generating a lot of resources per turn, if you've got cards there that can inflate.
The important thing to keep in mind is if the units or support cards you're playing specify a zone. Some only have their effect when they're played in the correct one. So if a card says: "Kingdom: Gain one (P) for each Development in this zone." And you play it in your quest zone, it won't gain additional power at all.
It sounds a lot more complicated than it actually is in game. Just remember you can eliminate yourself from the game by emptying your draw deck. So, the Quest zone can be tricky to defend and build up.