From my own experience, if you change within 24 - 48 hours of the flight, the EUA may not catch it. My tickets are Y26 fares and those are automatic upgrades at time of ticketing. Even then, it seems to take anywhere from a few hours to 48 hours for the upgrade to actually go through. When I've had a ticket issued within 48 hours of the flight, I really have 2 shots at the upgrade. The EUA window and the fact that it is a Y26 ticket. The EUA shouldn't matter to me as the Y26 should hit first but my point is that even with 2 ways for me to get the upgrade, it doesn't always show up before the OLCI window opens. I just do the OLCI and I get the screen that asks if I want a complimentary upgrade if available. I click "yes" and I get the upgrade. I don't know if this part is different for fares other than Y26. I would think that if you know there is availability and it is within 24 hours, then all the EUA's should have run. I would then think that if you do the OLCI right then, it should ask and give you the upgrade. If you wait to do the OLCI, then someone else who buys a last minute ticket might get it ahead of you.

Now I believe that Y26's upgrade to P and other fares upgrade to F, but I don't think that makes a difference to the OLCI as long as seats in F are available.