Very anecdotally, my feeling/experience is that fare class does make a difference for me. On the routes that I fly (typically between a hub and an outstation -- e.g., ABQ-IAH-DCA or BDL-ORD-ABQ), I usually get the CPU if I'm on a V or higher fare, and usually don't get it if I'm on an S or lower.

I'm also surprised at how often I'm #1 on the list -- which means I either get the last seat at the gate, or I'm the highest-status passenger in Y. And my CPU percentage was right at 50% last year.

All this suggests that I'm right on the bubble, and so fare class makes a noticeable difference for me (say, 80% chance of CPU on an E fare, or 10% on an N fare). But I may be among the more extreme cases. If you're Silver flying SFO-IAD, or a GS flying MCO-EWR, then it's not going to make a bit of difference.