If the phone that you purchased in China is unlocked, then yes, you will be able to use it, but if it is locked to a Chinese carrier, then no. If it is locked and you are travelling you will have to use the international roaming feature from your carrier.
If on the other hand you phone is unlocked, then you can use local sim cards in the phone, but you probably will not be able to get 4G reception, due to the frequency differences between countries. The phone will work, but possibly not on 4G everywhere and there will be nothing you can do about that. That is why different countries sell different models of iPhone to match their networks and why iPhone warranty is NOT international, but country specific.