I think Mental Boyfriend needs to ask himself "What do I hope to gain by telling my father?" and go from there. Does he feel it will in some way help his father get closure? Is he worried that his dad is somehow financing his mom under the mistaken impression that she's single and disadvantaged or something?
Basically, unless there's a good, helpful reason to tell him, I wouldn't recommend he sit him down for a "talk" about it. Mind you, that doesn't mean he should "keep it a secret", and he shouldn't think to censor himself if Steve comes up in normal conversation. ("What are you doing this weekend, son?" "Oh, Mom and Steve have invited me to come see their new house.") but really, since they're divorced, it's not much of his dad's right to know, either.