He was with the unit until their first engagement. My understanding is that the unit arrived on station on the Potomac down-river from Alexandria in mid-1862, and were told they would relieve a regiment that was loading and unloading barges and would receive their orders in the morning. The regiment commander marched them to the action in the rain overnight so that he would not be there to receive those orders in the morning. They subsequently fought the rear-guard action at that first engagement, and some were captured, including AE Cooley.
So you think he returned to Provost Marshal duties in Alexandria, perhaps? Is there a good source for records of those duties somewhere? It would be nice to even see some documents that his signature might be affixed to. He was a lawyer at this time, so would likely have had some sort of REMF duty (Viet Nam term, sorry). I have his bar certificate from New York State issued May 1860.
Thanks everyone for all your help. This is a great site.