The answer to your question is "Yes", with a qualifier.
Qualifier is "Brass life may be reduced somewhat."
This depends entirely on how much difference there is in the chamber's headspace dimentions.
What I would do is generate a half dozen pieces of fired brass from both rifles, marked for which one.
Attempt to identify which rifle drives the shoulder fwd. farther when fired.
If it is too hard to tell, pick a rifle (#1), full length size the brass, BUT work with adjusting the resizing die to only JUST reach the shoulder and push it back just barely enough to get the brass to re-chamber in that rifle. Absolute minimum resizing/shoulder moving.
Now see if it will chamber in the other rifle.
If it does, set that brass aside and back off the die, and repeat the process with the other rifle. You likely have already found the "tighter" headspaced rifle.
When you have just barely got brass to fit rifle #2, try it in rifle #1.
Once you find the "longer" rifle, set your brass to just barely fit in the shorter rifle. This way, firing in IT will strain the brass (stretching) the least, and firing in the other rifle will stretch it as little as necissary, but it will stretch more than the first rifle will let it.
Then you just have to make sure the ammo is compatible to the M1's gas system. Mil. rifles get designed to work around a very narrow cartrige profile (147gr bullet at arround 2800fps). Civ. rifles get much more "adaptable" gas systems. The difference in pressures betwen NATO and Civ .308, is little enough as to be pretty pointless. It's 2,000psi, at 60,000psi. 3%
Stretch happens when the firing pin drives the loose unfired case fwd. into the shoulder and holds it there while the primer detonates. The resultant firing pressure locks the case walls to the chamber, jammed against the shoulder, but the head of the case is too thick to "swell and stick" so it pushes back against the bolt face, stretching the brass just ahead of the head web.
My hunting rifle is a late 60's Browning BAR, .308, love that rifle. I almost exclusively use GI brass in it.