Mr. Ackley re chambered a .30 barrel to 8x57 Mauser. Yes, the .323 bullet was shoved into a .308 bore. Fired it with no problems. Accuracy was crap, but no pressure problems.
In this case, fools were buying ANY military surplus ammo for ANY military surplus gun... ["Don't all soldier rifles fire the same ammo?" Well, no... right up there with "shoots good, goes bang..." Duh...] Now the 8x57 in an '06 chamber where the case can split,... "loose gas" that causes problems and is DANGEROUS! HOT gas.
You should have no problems with a factory rifle. It is possible, low likely, but possible that the larger bullet might make the neck of the cartridge enough larger to be harder to get into the gun/chamber. With a bolt action and the "camming" of the closing bolt, you probably won't notice. In less "stout" actions, lever, semi auto, pump... then you might notice. luck.