If it was reasonably well established it might. i wouldn't give up on it yet. It's pretty tough. The main problem I've had with mine is that I don't separate it enough and it gets old and woody and sort of dies out.

Mine die back to the ground over the winter so I can't imagine that you've done it any harm. Wait and see.

Yes, wait and see. Some plants take a long time to recover if you cut the dead top growth back before spring. This happens with scented violets, agastache, and hardy penstemon in my garden. I won't make that mistake again. I never stop learning.