Sure, a .308 is plenty with a properly constructed bullet of sufficient weight.
That said, IMO, it is not an ideal choice. I no longer elk hunt, I really don't hunt any big game, for that matter, but did a fair amount of it when I lived in Wyoming. An elk is a damn big animal and most of the terrain in elk country, well, long or relatively long shots are common. I'm a firm believer using a round with plenty of horsepower for elk, personally, my favorite was a .338 Win Mag with a 225 gr. Nosler Partition, I also used a .300 H&H with 180 and 200 gr. Partitions.
I've never believed that magnum rounds are the the be all end all of hunting rounds; shot placement is king and bullet construction is queen, but I think that bullet weight and velocity are also important for elk.