I've had a few calls go to non-elite reps; it is very obvious when it isn't the Elite desk. I've had one non-elite rep tell me that they get calls when "there's no one at the Elite desk." This seems to be at times when Elites are least likely to call (e.g. late Saturday night).
When I have talked to non-Elite reps, it's never been too much of a problem, except once when I purchased a Y-fare, asked for the upgrade and was told after a pause "that's not available..." (agent clearly didn't know about the Y-up). Going online 5 minutes later, I upgraded in a few clicks.