Sure he should. Let the cameras roll, let the commentators comment, swing the club and become oblivious—BTW, that's something he's good at. Becoming oblivious, that is. He was obviously oblivious to the fact that he was married and had kids.
Look, I don't agree with his infidelities, and I do think his career is hurt, his earnings potential has been adversely affected, but none of this has a thing at all to do with golf. So, let him golf. The balls will fall where they may, and considering his past playing prowess, I think they'll fall pretty well.