Adding MR number to Priceline bookings
What I do is call the 800 reservations number after I receive my confirmed reservation from PL that is at a Marriott property. I make this call to confirm the PL reservation, and to add my MR number to my res on Marriott's record. I also do this with other brands (Hilton, Hol Inn, etc.)
Usually upon check-in, they will recognize your status, and give you the benefits associated with membership (free newspaper, etc.). Sometimes you get points for the stay, sometimes not...usually not nowadays. I have on a few occasions been upgraded to club/concierge levels immediately upon check-in with a PL reservation; I guess it depends on the occupancy load and the front desk clerk who is checking you in.
However, in most cases, you'll always get points for any incidental charges you incur over and beyond those covered by Priceline (i.e., restaurant/bar charges, room service, in room movies, etc.) Depending on the brand property you're staying at, some such incidentals are n/a for point accumulation.
Nonetheless, a handful of points from a PL stay are better than none!