I guess probably each company has its own policy toward Priceline tickets.
I had to fly on a Priceline ticket SFO-SEA, and I was given a seat on UA. Since I'm 1P with UA, I decided to stand-by for earlier flights. However, the gate agent refused to acknowledge my status, since it was a *gasp* Priceline ticket. Of course, I was not able to clear the stand-by, and wasted about 4 hours at the airport...

On my way back, I had to, again, stand-by at SEA. This time, the nice gate agent punched in my MP number, and I grabbed one of the two seats available for the earlier flight. (Still, the miles didn't post, as expected.)

Confused by the discrepancy between SFO and SEA, I sent an email to the UA customer service center, asking for clarification. They emailed me back, and told me that my 1P benefit cannot be claimed with a Priceline ticket. Then, they added "However, we are sorry to hear that the gate agent was not flexible enough..." I guess, as everything else, it depends... Oh well, you win some, and you lose some.