I would say it would depend on what you're upgrading FROM and TO. Others who've already upgraded that day, will be leaving some empty rooms available, and they may be higher categories than what you have.
I wouldn't hold your breath. We tried to upgrade from an inside to a window room and we were maybe third in line. No joy. There were no upgrades whatsoever. Ours wasn't even during the "peak" months of July and August for Alaska.
Is your PAT at 1 or are you arriving due to travel plans at 1? If your PAT is at 1, get there early if you want to try for an upgrade. If they don't have any, ask to move up your boarding group because you came early to check on upgrades. We do that at Port Canaveral. The upgrade desk has moved our boarding group each time. In March we had a PAT of 12:45, arrived at opening and boarded as soon as people were allowed on the ship. Can't speak for the Alaskan cruise though.
At 1pm, I would say chances are slim.
IMO, for port upgrades, you really have to be the first ones that check-in.
Also, most cruises sail full or near full so don't count on it. If there are rooms left, DCL will fill the empty rooms
with very low pricing (e.g. offerings to staff or interline personnel etc) towards the sailing date.
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