Will Pretrial Conversion Program show up on a criminal background check?

The answer depends on who the employer is. If you are applying for a job with a government employer it will likely turn up. There is a possibility that a non-government employer will also discover it in a background check. Most applications have a question asking if you have ever been arrested or convicted of a crime. Going through a conversion program is generally still a conviction because you wind up pleading no contest. If you fail to disclose it on an application and your employer later discovers it they will be justified in terminating your employment for lying on your application. It is best just to disclose it and explain. This advice is based on the limited facts that you have provided, additional facts may change the advice.