Not if the weapon is loaded properly, with the edge of the hand restraining the charging handle as the en bloc clip is inserted.
...the clip would clang loudly if it landed on a hard surface, alerting any nearby enemies that their foe was now out of ammo.
The Germans were quick to realize this and would often wait for that sound, then rush the poor soldier as he was reloading.
I have as of yet to hear of one documented case of this happening. I am not saying that it never did, just that I do not think it was at all common, and that this is a myth which has sprung up.
A fine rifle, much better for combat than what our troops are stuck with today.
I humped one of these brutes (M1) around in ROTC during the late 60's. I even bought a one in the 80's to shoot with. The "M1 thumbs" that I have seen were most often caused during drill when the the "inspection arms" command was given. The ROTC student would not completely lock open the action. When the "order arms" command was given the action would unexpectedly close as soon as the follower was touched by the thumb.