Nothing happens to the paint on the can, it doesn't get that hot. Here is the correct way to do drunk chicken:
Take an empty beer can and cut the top out of it. Fill it up with whatever you like, I usually use about 1/2 beer, 1/2 marinade.
Set the can on the grill and then put the chicken on the can. When the chicken falls over, he is drunk and it is ready(when the leg tendons are finished cooking, they break, that is when it falls over).