Should you? No
Will you? Most likely
Believe it or not, cheating is not as common a trait as day time TV and reality TV shows would have you believe.
I think what you're truly concerned about, given the way you've phrased your post, is "will he do it again"
The answer is yes, he will. Have you ever gotten drunk to the point where you started vomiting? What's the first thing you say? I WILL NEVER DRINK AGAIN!!!.....and you might mean it in that moment, but a few days later or the following Friday you're back with a glass in your hand because those feelings that caused you to drink the 1st time, WILL come back around, and again and again and again.
The same is true for people who have in that moment, justified cheating on their significant other. That feeling, that justification, that rationalization in which they decide to go forward with it, will come back again. Your boy may be sorry at the moment, and maybe even means it. But if it's whether he'll do it again, you know he will.
Because if he found a way to justify/rationalize it the 1st time, he'll find a way in that moment to justify/rationalize it a 2nd time.
I've counseled hundreds of people over the years. Some in your exact situation who went back to their cheating others, and some who decided not to and walked away. Do you know what every single one of the people who decided to go back to their cheaters regretted the most?
They regretted believing the other person could change but now the years they wasted by not walking away, the years they wasted by giving the person "one more chance", those years have gone and they're not getting them back.