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.
I've been thinking about this reply that I made last night and I spoke too soon. Out of the seven kilts I currently own, and the numerous others I have owned in the past, only one kilt gives me the problem of occasionally getting creased in the front. It's my lovat green Harris Tweed.

I have one other Harris Tweed kilt, and it's a lighter weight tweed, and it never gives me this problem. The lovat green is a very heavy weight. I don't know why that would make a difference, but this is the only kilt I remember ever having to iron out a slight crease in the front apron.

All my other kilts are standard worsted wool tartan, either 16 oz or 13 oz (though I have in the past owned everything from 10 oz to regimental weight), and none of them have ever had a crease in the front apron after hanging this way -- including one old MacGregor 8 yarder that I tend to wear only when I'm going to be marching in a parade and want the extra swish. So it will hang in my closet for months at a time and still not get creased.

I don't know why I only have this issue with my Harris Tweed kilt, and why with one and not the other, but there you go!