If you leave it hanging there for long periods of time, then yes it might. But each of my kilts gets a wearing about once a week, once every two weeks at the least, and only rarely do I have this problem.

And when I do, it only takes a few seconds with the iron to get the crease out of the flat apron, versus all the time of re-pressing the pleats if it had been folded the other way 'round.