It's a matter of public record. It depends on what kind of background check is run. They can vary quite a bit.
Please be advised that any answers or information disseminated above do not constitute legal advice and that the attorney responsible for this posting is merely attempting to participate in a Q & A session intended to be helpful but certainly not intended to be legal advice. It is important that you understand that no attorney-client relationship has been formed and that the attorney has no obligation to follow up with you with your legal issue unless you separately contact said attorney and arrange for him to legally represent you.
If the background check is only for criminal matters, it will not show up, but if it is for all court matters, it will show up. This is part of the public record and will always be.
R. Jason de Groot, Esq., 386-337-8239