If you take away the timey whimey stuff, that makes the question a little clearer. The question would become,
"Is it possible to cheat on someone with themselves?" and the answer is... Yes. Cheating is a betrayal, so if someone was or felt betrayed, it's cheating.
For it not to be cheating, all four(the time traveler, their wife, and their younger selves) people would need to be aware and consent to the arrangement.
Though some people could be removed and make it not cheating. For instance, the wife Person B dies before the time traveler Person A goes back in time, meaning only the time traveler Person A and the two younger selves clone(Person C) need to consent. If the two younger selves aren't dating/married yet, then the younger version of the time traveler has no say in the matter.
Oddly, the situation I thought of when reading this... Let's call them Alice and Bob. Bob goes back in time, and young Alice gets pregnant. Old Bob then disappears, for some reason, and Young Bob steps in to help Young Alice raise the kid, thus creating a... Let's call it self-fulfilling prophecy. Vaguely
Like this.