No, It won't hurt the tree. As a matter of fact, that's what I do. I leave the top 6 steps in, and take the bottom 5 or 6 out, and replace them each time I hunt. The only problem that I know of was a few years ago, a buddie of mine went into his spot, and started putting his steps in. He got about 6 ft off the ground, and one of the steps "pulled" out. Turns out some "claim jumper" used bigger steps to climb into the stand, and as a result, "widened" the holes.
As long as no one does that to you' you'll be fine.