Not normally. As I recall there are factory "notches" in the fenders for clearance (think that's '33-4, could be CRS though), but in stock configuration the only other "support" for the radiator are the two brace rods from the upper tank bracket to the firewall, otherwise it "floats" in there. Of course the grille shell fastens to it as well, there should be brackets on the radiator sides to hang the grille retainer brackets.