Ive never tried in a city that did not have the gate display but as soon as my name became #1. I wait a little longer untill it seems boarding was mostly complete. I say i'm #1 on the upgrade list and if F has boarded in full. Note they may interpret you asking as checked in full but you only care about boarded.

Just dont wait untill too late through I almost missed a flight becsaue GA refused to process the upgrade list even though it was time for him to close the door. He finally said take 1C even though i was not on the manifest in that seat (according to the FA after take off). luckily per @DeltaAssist he reflected the seat change and that i had boarded after we were already in air