Negative, ghostrider. Any award travel does not accrue any type of miles, EQM, RDM, or EQPs.

EDIT: Assuming you are using airline mileage to redeem. There are some credit card programs that let you pay for tkts using their miles/points (i.e. SPG Amex, Certain Capital One Cards, and others), and this is essentially a revenue ticket, with all the rights and perks of one.