Originally Posted by Demise

It really isn't. AP doesn't clear any prior unlawful presence and doesn't count as admission for purposes of 245(k). In fact it's probably a bit worse since if you enter on parole you're an "arriving alien" or "applicant for admission", meaning that you actually do not have the right to having an IJ review an I-485 denial and ICE can actually issue a removal order against you on their own. It might be advantageous with that an "arriving alien" can file for AOS with USCIS notwithstanding a removal order or pending proceedings but travel with AP while in proceedings or subject to a removal order is pretty much unsafe.

Basically, you don't have much to gain from doing AP as an overstayer.