Because you aren't a UA elite I'm going to guess the answer to this is no, but do you have a subscription to ExpertFlyer? If so, get on there and set an alert for "P" on that flight now. Do it and you won't have to check United.com expert mode every few hours to see if "P" opens up.
Several on here warned you it would take a few calls to get this to work. Glad you persevered. Question is..how did you call the 1K line if you have no status? If you dialed that number and used your FF# then you were transferred to a regular agent. Maybe you called from a friend's phone who is 1K and it recognized the number?
If you don't clear in advance and wind up waiting for a first class seat at the airport it's truly anyone's guess where you will wind up on the airport upgrade list. It can be anywhere from #1 (your rightful place assuming you are the only displaced F passenger) to not appearing on the list at all since your waitlist for "P" will have expired and you have no elite status with UA. I'm more hopeful "P" will open up for you before the flight. I have more confidence in UA's system to clear you automatically into "P" if the class opens up than I do them adding you to the airport upgrade list in the correct order, or even at all.
Let us know how this unfolds up until the flight.
-RM