If you have the ammo on hand, I would try it and watch for anything like pierced primers, hard bolt lift, or ejector marks on the case head. If nothing like this happens, carry on; if it does, discontinue use. Practically speaking, most factory .223 chambers will have a long enough throat to handle 5.56 and you will likely see some sort of warning sign well before catastrophic failure if you pay attention.
That being said, I would not have any sort of accuracy expectation out of Norinco 5.56 ammo, nor would I seek it out for a bolt gun. The case I bought was acceptable cheap blasting ammo for my AR with reloadable brass, but that's about it.