From what I've read, he hasn't.
Once, he was given a rut inductor, but he had s3x with the boyfriend. The thing is, because of the drug, he didn't really remember much of the night and ends up thinking he slept with a random omega. Then he confesses this happened to the boyfriend and break up the relationship, as he doesn't feel it's fair that he cheated.
Also, just to add on top, he feels very guilty for (thinking) he slept with another person, but even more that the few memory fragments of the night he has, the omega has the boyfriends face. Because of the trauma e keeps throwing up whenever images of him having s3x with the boyfriend come up.

From the comments, I can see that the alpha is attracted to the beta but can't express it due to trauma and, as a result, indirectly hurts the beta.
But can I ask if the alpha sleeps with anyone else while they're together? Cuz it feels like he would have (slept with an alpha/omega), if he doesn't sleep with the beta during his ruts. Just want to know before reading (not a fan of a sleeping-around alpha top ╮( ̄▽ ̄)╭)