I'm charged with identity theft, prosecutor has agreed to dismiss charges only with restitution, will this show on my record

The arrest might show up, depending on who does the background check.

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

If charges are dismissed, you should have no criminal record. Only a deep search might show the arrest.

I guess the question is for a search to who ?

If the FBI runs a check, of course they will find it, but of course for a regular employment background check, ran though a government agency, it will not show up.