I've had winning bids for Hertz, Avis, Alamo, National and Budget. I am enrolled in each of their "express" services.
I've called each company and there is NO way to add your number to the Hotwire or Priceline reservation PRIOR to arrival at the facility. At the facility, most times, I've had no problem using the "express" desk or office at most locations rather than standing in the normal line.