I have a rubber roof on a building and in the winter the ice dams up the drains on the low end of the roof. Could I put some road salt on the roof to keep the drains from freezing?

I have no practical experience in this area, but as a chemist that has worked with rubber, I can't imagine the salt hurting the rubber.

Note, may not be the best for a metal gutter.

It should be fine but try calcium chloride rather than sodium chloride. It will continue to melt at a lower temp than sodium. If you have time read this. Calcium Chloride (CaCl2)