Yes, she will. She may prance around looking for her babies, and be quite irritable to everyone - but after a day or two she'll be just fine. The babies will cry for her for a day or two as well. But then they'll settle into their brooder and be just fine. Unfortunately, this means you'll have to go through the integration process when it's time to re-introduce them to the flock. Mama absolutely will not know they are hers.
We have a few small cattle farms surrounding our place, and one larger operation for feeder calves. Every spring and fall, when they separate the calves from their mothers, the bawling and crying and mooing is NONSTOP for four days!!! My heart aches every time I walk out the door during this time. The first time I heard it, I was so alarmed that I drove down the road to see what the hell was going on... and saw a holding pen with maybe 100 crying little calves, surrounded by as many bawling mamas. ... silence of the lambs comes to mind. Last week, just as soon as the calves and heifers from the feeder operation quieted down, the neighbor on the other side of us decided it was time to separate his as well... and it has started all over again. aarrrggghhh!!!
We don't normally separate ours like that (we have less than 10, and they go to our feeder pasture much later), but there have been a couple of times I had to separate a mother from her newborn for health reasons.... it's awful.