I have done quite a few on the kettle using indirect heat and no brine. I always look for a smaller 12 pound or so bird and it always took 2.5 to 3 hours.
I picked up an "natural" bird with no additives today and I am going to try the brine on it and cook it with an injected bird on the WSM to see if am am missing something good. The fresh bird was over twice the cost of the injected so I hope it is worth it.
Cooking with a classic kamado Joe