David--
A pan won't retain moisture. A pan can buffer the heat, slowing evaporation or, if you cook immersed partially or fully in sauce, slow down evaporation.
Hard to brine whole or halved chickens partially. It's possible to brine just breasts if you cut the chicken up. Brining will give you a little more margin at the finish. It won't slow the cooking down so that the breasts finish at the same time as the thighs.
I cook direct on the grill (high heat, no pan if using the WSM; high heat indirect if using the kettle) because I prefer chicken cooked quickly and prefer crisp skin (I cut the chicken in pieces and pull the breasts when they're done, as noted above, or cook all dark meat pieces or all breasts). You might consider Paul's and Randy's suggestion to low/slow your chicken and see what you think. Many people like that approach and will brine, flavor-brine or marinate ahead of time for added flavor.