The answer may be as to the nature of the background check and where it is done. If it is in the same county, a look through the court records wi probably reveal the fact of the court proceedings. If it is a different county, probably not.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
The only way to know for sure what is says is to order a copy yourself. Go to the DOJ website and find the forms to get a copy of your record. You will have to get a livescan done and pay for it but that is all. Depending on if you were arrested or just cited there may be a record of arrest on your rap sheet. Infractions shouldn't apear but since you were charged with a misdemeanor originally there may be an entry for the charges. Most jobs can't/don't require disclosing infraction convictions so be sure you read the question thoroughly.
Because it started off as a misdemeanor that was subsequently reduced to an infraction and then dismissed under 1203.4, yes, it will likely be on your rap sheet. The question is whether or not your background check will turn this up. If you have to go for fingerprinting, it will show up.
However... most private employers cannot consider a dismissed case against you, so if they find it, technically they're not supposed to consider it.
That's how it's supposed to work, but . . .
If you're concerned that it will be found, many people choose to be proactive and disclose it and put the most positive spin on it you can - that it was reduced, you paid your debt, you learned, etc. You can try to do whatever you can to show you've changed since then (proof of volunteer service, character letters, etc).