Will a legal diversion show up on a background check?

Maybe. If the person fulfilled his or her mandated obligation (community service, monetary restitution, etc.) in lieu of serving a sentence to the satisfaction of the court it is possible the record would be expunged. It really depends upon the length of time since the application of the diversion sentence, the laws of the state where the act was committed, and the prior history of the offender. First of all, all you have to do is google a question like "Will diversion appear in criminal record?" State laws vary. However, a diversion -- suucessfully completed -- will appear on your history as a dismissal of charges, so yes, the record of arrest and court appearance will show up in a background check. If the diversion wasn't successfully completed, it's as if the original divresion never happened and the full charges stand.