I believe so, but I'm not 100%. Had a buddy that said it was fine one time, but I was hesitant. I did some research online and from all accounts it seems that 7.62x51 through a .308 is fine, but not to fire .308 through a 7.62x51 because commercial .308 is a higher pressure than 7.62x51.
Found this thread from the OB:
7.62 NATO
Posters agree that 7.62x51 is fine through .308. It's the same round, just 7.62 is lower pressure