This hasn't happened yet but I think it could.
I'm pumping to establish a freezer supply and I wake at 5 am to pump since I have to wake up at that time when I go back to work. Sometimes my LO sleeps great and will wake only once about 1-2 am to eat (he's 11 weeks old).
What should I do if he wakes when I'm in the middle of pumping? Do I give him the milk in the bottle or just feed him from my breast? I hope this never happens but I want to know what to do in case it does. He gave me a little scare this morning when the baby monitor went off.