Well the opinions run the gamut. I would say no. Though I have read a lot that would contradict me; I know I would resent my wife and run to the OW if she did that.
Yes at the start there is a thrill of the "hidden" of the affair. However, at least for me, I wanted people to know. It was such a stress living a double life. It would give me a normal life if it were out in the open.
I think if you do that he will run to the OW arms. He will feel vunerable and guilty. He will have no other opiate or no where else to run.