When I was assigned to the Coast Guard recruit training center armory, we had HUNDREDS of M1's which were issued to recruits for d & c practice. I don't recall ever seeing one with a serialized stock.
Sad part was, some of those rifles were perfect and with four, yes four, digit serial number receivers. All had been "de milled" with a tack weld at the barrel to receiver, and bores filled with lead. We had rifles from all manufacturers that ever made them. Almost made me cry to look at them.