Go for it.
Post #2 has it backward, the 7.62x51 is higher pressure than .308Win. However, I've done it quite a bit. The bolt will occasionally be a little stiff to lift after firing, but nothing extreme like stuck bolt, ruptured case, etc. The recoil is noticeably different, too. If I go through 100 rds. 7.62x51 at a single range session, I get a bruised shoulder. Commercial, not so much.
I stand corrected. I will relay my experience has always been that milsurp ammo headstamped 7.62 makes my bolt stick and shows the occasional flattened primer. My rifle seems to like a combination of Argentine cases, Varget powder and speer bullets. I shoot a lot of surplus ammo for cases and have pressure signs, albeit mild, with every single shot. Opening the bolt after firing commercial or reloaded ammo is never as stiff as with the milsurp. Never had a flattened primer, either. So a logical question, from my viewpoint: Why would a lower pressure cartridge loading show higher pressure signs than a lower pressure load?