Better answer - it depends. If you literally mean "damp" as in "a little rain got on it", then No. Did you land some distance from the hanger then walk back in a downpour? Then maybe. After water jumps where the skydiver wearing the gear is actually in the lake for a couple of minutes the reserve is routinely opened, aired out until dry, then repacked. This doesn't cause any damage.
(This post was edited by Bertt on Jan 12, 2013, 8:38 AM)
I have unpacked a reserve that was soaked in beer for a couple days. The beer left brown areas that felt stiffer than the rest of the fabric. It cleaned up with cold water, passed the acid an strength tests, and got repacked.
As for jumping in rain, I don't worry about the reserve, just dry the main and pack it.