It shouldn't be an issue as long as you call/email the hotel beforehand to let them know that you will be arriving after midnite. That language is mostly there for when there is a multi-nite stay and the guest shows up to check-in mid-trip... after the first day the hotel may have already marked you as a 'no show' (and on very busy dates may have re-sold your room)
However, since you have some time before your trip, i would actually take a two pronged approach:
1) call the hotel informing them of your after midnite arrival, ask them to note it in the computer so that you're not viewed as a 'no show', and get the name of the person who you spoke with
2) a week later send an email "I have an upcoming stay (provide details, including dates so the hotel can look up your reservation) and have previously called the hotel to let you know that my flight does not get in until after midnite. Can you please confirm that this is marked on my reservation so that i'm not viewed as a 'no show' and i won't have any issues when checking-in. Thank you."
You could reverse the two above, but i prefer to talk with somebody first as it helps ensure that it gets done (especially when you ask for the person's name who you are speaking with) and then follow-up with an email so you have something in writing should there be any issues. If you're very concerned you could also call the hotel on the day of travel/arrival and let them know that you are on your way and due to arrive after midnite, so please don't mark you as a no-show.
If you need help with this trip feel free to start a NEW TOPIC in the CALIFORNIA >> Priceline (San Francisco) section of the board and we can provide you a bidding strategy there to follow. Also, as priceline is constantly moving/hiding the 'Name Your Own Price' bidding form, you may want to bookmark BiddingForHotelRooms.com for quickest/easiest access to their bidding page.
Good luck... please remember to post your win or let us know how we can be of further help.