dabuk said:I'm sure that legally there is an issue. Whether they have an issue at the POE or not depends on the immigration officer at the desk, since you can no longer be admitted as a non-immigrant (so your H1 is useless), and without AP/GC in person, they can deny you admission.
My point is why take risk, when you can avoid it? Apply for AP, get AP, travel.
"Given the unpredictability of processing times, it is possible for the I-485 to be approved while one is traveling abroad. Therefore, although H-1/H-4 and L-1/L-2 holders can travel without advance parole, it is best not to do so. This is particularly true for individuals who do not have valid visas in their passports. If the I-485 is approved while an individual is abroad, s/he is no longer eligible for nonimmigrant (temporary) status. The best situation is for the individual to have advance parole, which makes travel possible, and to explain the fact of approval at the Port of Entry. The worst situation is if an individual does not have advance parole and plans to obtain an H or L visa at the consulate for reentry. If the I-485 is approved while this person is abroad, s/he is not eligible for the H or L visa at the consulate. Without other documentation permitting travel, one would not be allowed to board the plane without a travel document or valid visa stamp in the passport."
http://www.immigrationportal.com/archive/index.php/t-203925.html
This is from one of my co-worker true experience and also from my lawyer.
Yes AP is a must, otherwise whole greencard is doomed if 485 gets approved when a person is outside united states without a valid AP.
H-1/H-4 is no longer valid after 485 approval. You will be stuck at POE or at later time.
It's better to consult lawyer before travelling outside with 485 pending as each and every case is different and unique. Do not take risks at final stage after a long years of wait...