I wouldn't leave it in the brine, you'll risk over-brining it which can also lead to bad texture.
It should be fine air drying in the fridge for a couple days, but I find that the skin doesn't dry well in the hollows between the legs and breast, and the like.
I use a hair dryer, dedicated to the purpose of even drying poultry before it goes into the oven, or spit, or the like.
The couple days rest will also help equalize the salt throughout the bird.