It would make sense...steel against naked skin is only sexy when there's romance involved; in battle armor its like you're just asking for it.
In reading Cornwell's books, he makes a case of wearing fitted leather garments that have been greased underneath plate armor so that there's no pinching and the plates can shift about w/out chafing the skin its supposed to be protecting. But he never really mentions anything about padded undergarments or gambesons- almost as if they didn't exist or maybe they just didn't exist for him. He seems to have gotten most of the other stuff correct. He also mentions leather-backed mail on more than one occasion...and that would seem to make sense to me too. But its just historical fiction- so naturally you take it with a grain of salt but a lot of what he'd written just seemed right to me.