Here is how it has been recently working for me. The fare basis for the tickets bought by Global Travel have been showing up in the Delta reservation system as an equivalent to a Y-0 (Y-zero) fare. At NWA our tickets used to show up as an equivalent to a Y-26 fare. Those fares would be swept by the computer and upgraded ASAP after being ticketed.
I have called Delta on the Elite line and mentioned the Y-0 fare and requested to be upgraded and they have been upgraded on the spot if seats are available. There is no need to wait for the elite upgrade. Call and you will be upgraded once the reservation is "ticketed" or paid for is a better choice of words.