Sort of, technically, no state needs more than 20 moves to be solved (but finding that optimal solution is kinda hard for humans). So while luck can play a part (i.e.: you may get a configuration that only requires three moves), it's much more a matter of skill to find those 15, 20, 23 moves.

http://www.cube20.org/ https://www.youtube.com/watch?v=yF2J39Xny4Q