Yes, it's a perfectly good idea to breathe for them ASAP, even if it's assisted breathing. Get that O2 out quick if you have access to it too. Here, we give two slow breaths at first, (2 second length, 3 second spacing)check pulse and then continue 1:5, O2 at 10L/min. (& Call the Ambulance!)
The question as if they've BO'd and no aspiration vs Aspiration, is likely a matter of timing/airway protection- if they come to, they can still experience dry-drowning. read
http://pedsccm.wustl.edu/All-Net/eng...ct/drown-2.htm
Chest compressions can be done on a weak pulse, but definitly use caution, keep on top of the vital signs so you know which way they are progressing.