I don't think status matters at all. I was on a CO flight a couple of weeks ago that was running rather late. There was a later flight that was going to leave earlier and I wanted to fly standby on it. Despite having a paid first class ticket and being elite, I was told that I would have to go at the end of the standby list of 30 or so people, including a bunch of people with NW tickets.
I think CO's standby policy needs some work. Why should a paid first class ticket have to be at the end of all of the coach standbys?