I don't live in a country that this app is available but I am purchasing my apple watch in the US. Can I download the ECG app and pair with phone in the US and then have them shipped to my country for use? Can it work this way?

1. You cannot order an Apple Watch from the US Store and have it shipped to your country. Apple does NOT ship internationally
2. You will not be able to use the ECG app in a country where ECG is not approved
3. If or when ECG is approved in your country, then and only then will you be able to use it
4. If you purchase a watch in the US, which is cellular and don't live in the US, Canada, Mexico or Puerto Rico, you won't be able to use it as a cellular watch outside those countries
5. A watch purchased in the US will have no warranty outside the US. Should you need warranty support, you will be required to bring the watch physically to the US for service
6. Don't buy your watch in the US. Buy it in the country you live and will use it

you can load any app, which is in the app store of the country your Apple ID is linked to, not from the country you are actually located in.