If you make sure the body seams are watertight from external road water before you apply the sound deadening material there should be no problem.
Of course it should go without saying that if you have a '30 model car which had drain hoses from the cowl vent, windshield, rear windows, trunk lid and quarter panels, you had better make sure that the drain holes are clear and that the hoses exit the body. If water gets into the car it must have a path to exit the body.
I have used the Dyna-Mat, Road-Kill products on several cars, the stuff is very user friendly and works great.
Starting in the mid '30's all of the original manufactures used sound deadening products in varying degrees. Ford liked a fabric material that looked like a treated cloth or heavy tar paper. They also used a tar like product that mostly turned brittle and lost bond to the metal panels. The fabric/heavy tar paper products also came loose, wadding up in the bottom and trapping moisture in the quarter panels.
Be very careful not to use roofing products to seal up and/or deaden the body.. If you do, in short order you will be overpowered with a chemical smell