No, AppleCare+ only has to be purchased in the same region as the product.
Service Options are available wherever offered, as I stated previously when quoting the T&C:
”Please note that if you seek service under this Plan in a country other than your country of purchase, the service fee will need to be paid in that country’s currency and at that country’s applicable rate – for further details, including regarding applicable fees by country, please visit the AppleCare+ support website at apple.com/legal/sales-support/applecare/applecareplus/“
In other words, as long as you have your AC+ plan purchased for the product, you can get service done on the product in all eligible regions that offer service for that product.
If I purchased my iPhone & AC+ in the US, travelled to Singapore for vacation and dropped my phone, the screen cracks, then I would simply set up a service request in Singapore to have it repaired, paying for the service in Singapore’s currency and the fees associated to the service for having it repaired while in Singapore. I’m not sure how else I can convey this.