The plenum above my basement installed updraft Gibson KG6RC furnace in cooling mode is sweating profusely. Cooling seems to be working fine, and drainage tube from plenum seems to be draining normally, but I worry that the condensation on the outside of the plenum will rust the furnace out as it seems to filter its way down the outside and through the cabinet to the floor surrounding the furnace. Should this plenum, be insulated? If yes, should I use foil-faced urethane and glue it to the plenum?

High humidity in the basement will cause this to happen. When the moisture hits the cool plenum it condenses. Insulating the plenum will be a big help in preventing this. Also make sure the drain is running free and if push comes to shove a dehumidifier installed in the basement will help remove the moisture that is causing the problem.