If AppleCare+ is available in that country, “generally” they will take care of it. There are some exceptions that deal with hardware differences; e.g. you might have to accept the local model as a replacement (which for example, could be eSIM-only in USA vs pSIM-only in China or eSIM/pSIM combo elsewhere).
If you’re visiting a country where AppleCare+ is not offered, then you will not get any benefit from AppleCare+ in that country. You’d have to put off the repair until you return to a country where it’s supported.