I've shot .223 in my Rock River AR-15 that is marked 5.56 without any problems.
J
ust for clarity, you can always shoot .223 in a 5.56mm chamber. You can't necessarily shoot 5.56mm in a .223 chamber because it has a shorter throat.
The increased pressure causes cycling issues in gas guns. In a bolt gun, I don't think it would be as much of an issue.