I can confirm that United's app for Android (and I'm 99% sure iOS) will show where you are on the list - it works just like those gate display monitors, except they simply say if first and economy are available or not (as a yes or no, not an actual number). However, you can get an idea by looking at the seat map (also on the app). At that point, most people would have checked in and have their seat assignments, so it's actually reasonable to do that compared to as a way to plan which flight to take.