If you are buying a typical "shrink-wrapped" turkey - that is not marked specifically that it was not brined or injected - don't waste the effort to brine.
But - you can place it on a wire rack above a pan and leave it exposed to the air in your fridge for at least one day - or 2-3 as long as you keep it below 40F.
Then, when you bring it out - the skin will crisp much better because much of the excess fluids in the skin will have evaporated. The turkey will not be dry tho - the injection/factory brining will ensure that.
Before putting it in the PBC ( and I would say use wood chunks if you want any wood at all...chips will burn up too quickly...) spray a very very light amount of oil on the bird, and apply your rub/seasonings.
Go have fun - the pictures, and share your experiences with us!