My wife needs to travel back home due to family emergency. TPS has been approved, AP approved 2 days ago but no further changes in notice. We are hoping that AP will arrived at least with in 2 weeks. But, this travel is urgent. I was thinking if it would be OK to leave and I mail the AP document later after the arrival. Other forums have reported this kind of situation and the traveler was able to get back to US (under the condition AP was approved before departure). Our status is F1/F2 but VISA expired 6 months ago.

Any one else has this kind of situation. 

The AP will have a start date and and end date.
Also they will give you two copies keep one and mail the other.

You should fine I think. Also i suggest you travel back with port of entry cleared in abudhabi ...lot easier