If you look at the USCIS advance parole's instruction form, it says "DHS may issue an AP document to authorize an alien to appear at a port of entry to seek parole into the US. The document may be accepted by a transportation company in lieu of a visa as an authorization for the holder to travel to the US. However, warning: The document does not entitle you to be paroled into the US; a separate discretionary decision on a request for parole will be made when you arrive at a port of entry upon your return."

It means, AP should work just fine, even if the visa has expired. However, if you have any thing bad in your background history then you will have problems.