I did the same thing last week - signed up for a PC membership right before travelling. The representative I talked to warned me to print out the receipt/confirmation email and bring it with me, since I would be flying Delta and hoped to use the Crown Rooms. Technically, they don't have to let you in to the CRC until you receive the actual card, but with the receipt and boarding pass, I had no problem in LAX, SLC or ATL.

But, if you are just on CO and using PCs, they should have yoru # in the system [though the printout could be a good safety net].