I would not use 20 gauge buck on a deer, except in very close situations. I have a buddy who hunts in the middle of a forest, where there are no shots over 20 yards. He aims for the neck and it does the trick.
But i have nevr tried it on deer. I use it quite effectively on coyotes and red fox out to forty yards out of a 20inch Mossberg 500 barrel. But for deer i would recommend Winchester Supreme sabot slugs, if your son's shotgun has a rifled barrel. With these, out of a fully rifled barrel, i have taken 180 pound deer at 100+ yards. They have outstanding knockdown power, great accuracy, and manageable recoil. They are quite spendy (around 13 bucks for 5) but definently worth it. i hope this was a help.