If you go to the link below, a PDF of the M4 manual will be downloaded.
On page 5 it reveals that the tripod bushing is 1/4 inch. This indicates that there was at least one version of the M4 with that diameter tripod screw so its as likely as not that your base plate is original. I do not know off hand when the change was made. My old M3 of course had the larger bushing but when I got it, it had an adapter screwed into it to facilitate use with later accessories.
But I know that later black M4s had black chrome bodies instead of painted enamel. Its possible this was another change made at the same time but its also possible that the change came earlier maybe with the M2 - the Leicaphiles will no doubt know this detail. It is also possible (??) that the 14405 grip was available with alternative screw fitting for different Leica M bodies. I don't know this detail either and am guessing but it is logical. I had an aftermarket grip on my M3 and it worked and looked just fine. It had as I recall the smaller 1/4 thread which I used on the M3 with the 3/8 adapter in place.
"AFTERTHOUGHT: If the 14405 grip came standard with a 1/4 screw could it be possible that the 1/4 to 3/8 adapter thread that I mentioned above might still be mounted on the screw in your 14405 grip when you bought it? It might be possible if you check closely. Usually this adapter is found inside the hole in the camera baseplate, but there is no reason one supposes why it could not have been on the thread on the grip instead. If so you should be able to hold it with a suitably protected pair of pliers and take it off.... maybe give this a try."