I think that brining will certainly affect the skin later, because it hydrates the skin more and adding more moisture will make it cook differently than NOT adding more moisture to it.
Now how MUCH does it affect it? I don't think a lot. In fact, I think brine or no brine, if you cook one bird low and slow in a 250 degree smoker and you cook one bird in a 375 degree smoker, the first one (lower temp) will have a more rubbery skin, while the higher temp one will have a crispier skin.
One way to help with the superhydrated skin after brining is to remove the chicken from the brine and put on a wire rack in a pan or on a sheet and leave in the fridge UNCOVERED for a while to DEhydrate the skin and allow it to tighten up. I leave whole chickens and whole turkeys in the fridge like this for a couple of hours to overnight if I can to allow for this.
Either way....as said above.....TEMP will more affect the skin than brining.
Now....depending on if you're looking for "bite through" skin or "crispy" skin.....there are many other factors that will affect both and brining is the least of your worries.
See.....^^ THIS ^^ is because the salt used in "dry brining" will remove the moisture, while imparting flavor, in the skin. He gets a crispier skin because of the lack of moisture. SO, it follows, then, that by ADDING moisture to the skin by wet brining, you'll affect the crispiness in the opposite direction.
This is why dehydrating the skin will help with crispiness while the brining process will still greatly affect the actual meat of the bird.
