Yes. If I recall correctly 7.62x51 carries a slightly lower maximum pressure than .308, so 7.62x51 is perfectly safe in a .308 chamber. Maximum velocity reloads might be a different story, putting .308 pressures in a chamber designed for a lower pressure doesn't sound like a great idea, however the difference is small and the two are basically regarded as interchangeable.
Thanks for that link, John! I had it in my head that the .308 was the lower pressure load to the 7.62x51 much like the .223 is to the 5.56x45. Learn something new every day.