I knocked off most of a cayenne plant early this season with the weedeater. There was a little stem left with a few nodes so I let it go, now you can't even tell except for the fact that it's peppers are a little bit later to start ripening than the rest of the plants.
I put mine out too early last year and they got nipped by the frost. They turned completely black, dropped all leaves, then sprouted back out. Pretty darn tough as long as you don't kill the root.