I have a slightly contrarian position, and I've posted this multiple times, but so far, I seem to be the only one that has experienced this.

I have found, that if A) your upgrade has not cleared within 24 hours of departure, and B) you check in online, your UG request will get transferred to the airport list, and the priority to clear follows the list that others describe above.

However, if A) your upgrade has not cleared within 24 hours of departure, and B) you check in via an airport kiosk and manually select for your name to be transferred to the airport list, I have found that your name will mysteriously disappear, and not get transferred - effectively reducing your UG chances to 0%.

Several gate/ticket agents have shared with me anecdotally that they've heard this many times, and something is wonky with the functionality in the kiosks, under certain unknown/undisclosed conditions.

So, in my experience, checking in online will not increase/decrease your chances, whereas checking in at the airport cannot increase your chances, but can potentially decrease.

ymmv