It won't kill a tree, and if you leave the steps in for a long period of time the steps will actually get harder to unscrew out of the tree. Actually, doesn't take but about one season for the steps to get harder to remove.
Will the steps eventually rot, probably. BUT it'll take many years for that to happen.
One thing I do to make them easier to screw in is to use a short piece of 1/2" pvc pipe that I slip over the step and this allows the step to rotate easily while I have some thing to hang onto firmly as I screw them in.