No- and besides, many damasks (I think) would sulk in your climate, in general the once-bloomers do much better with a dormant season, and damasks don't appreciate high-heat high-humidity.
If you want a fragrant rose to do root over rock, I would try to track down 'Sweet Chariot'. It is a miniature rose of the polyantha lineage, so it should have no problem ramifying (unlike many roses) and the color is cool, too.