I suspect it depends somewhat on the type of upgrade.

Recently (ie this year) I have found that when on the waiting list for cert type upgrades, they are often processed at the last minute at the gate. I have had op-ups given to me at the check-in desk, handed to me at the gate during boarding and once(!) after I was already seated way in the back of economy. Pretty funny actually - one of the crew asked me what I was doing when I started heading to the front after everyone had cleared the aisle.