I have consulted with my O-1 attorney on returning to US by using AP, she definitely answered that my O-1 would be invalid if I use AP. I have found lots of posters in this forum on this issue. Most people said AP acts as a visa and would keep the same status (H1B, O-1,etc) if he/she works at the same university/company upon returning to US by AP. I have to clarify this issue. The following email is from my attorney:
If you use your Advanced Parole when returning to the US, you by using the Advanced Parole are withdrawing your O-1 nonimmigrant status. You would then be considered to be an Adjustment of Status pending and would be working using your I-765, Employment Authorization Document (assuming you have applied for this based on your I-485, Adjustment of Status). We always advise our clients to obtain a Multiple Entry Visa (in your case- based on your O-1) in order to travel.