are you sure?

Here was my lawyer's response:

If you re-enter on Advance Parole then you MUST also have a valid EAD work card to allow continued employment (your prior H or L visas will remain valid but not “active” and thus the EAD is needed to allow continued employment).

If you show the INS inspections officer the Advance Parole to re-enter, then you will not be admitted as an H-visa or L-visa holder, but rather as a “Parolee” and this classification will be stamped on your new I-94 card.