As a Hilton HHonors member, I get Hilton HHonors points on incidentals only, even if I am on an awards stay. The points are based on the dollar amount which I have spent on a visit. Fewer dollars spent mean fewer points, but yes, I still get points. In addition, I even get credited the stays and nights towards elite status for the following year!
Different hotel programs may have different rules. I say go for it and ask. The worst that could happen is that you will be denied. What do you have to lose?
To which hotel program(s) are you referring, DaDOKin DC?