I usually check seatcounter before day of departure to see my chances. If there are at least 2 seats open, I would check with the GA.
With that said, as an SE, I was #3 on the list on a MSP-SFO early evening flight. The GA said there are quite a few PE's under me and she's not sure how my name got ahead of them. I actually glanced at the list and there must be at least 20 names on there.
So yeah, it's worth a shot