ngl, I kind of wish Chi chi's affair would have lasted longer in secret, without anyone knowing. But considering this is DB, it was only a matter of time until someone sensed her Ki hanging around a stranger at odd hours of the night and morning consistently for several hours. Though considering how depraved Chi chi is in this game, one doesn't need ki sensing to find out she's been sleeping around.
Knowing Goku, he probably might not even care much if he found out, so long as Willy ain't harming Chi chi or worse kill her like Zamasu did. Now that I think about it, I think so long as the homewrecker was a super chad fighter who could go toe to toe with Goku, he might be included into the family with open arms. So long as he continues to give him a good fight.
I can already see Goku just interrupting their cheating session mid-thrust, begging the guy to hurry up so they can fight because Vegeta is too busy with something else.