It should. There may be limitations however. This is part of the US warranty terms:
Apple One (1) Year Limited Warranty
Apple reserves the right to change the method by which Apple may provide warranty service to you, and your Apple Product’s eligibility to receive a particular method of service. Service will be limited to the options available in the country where service is requested. Service options, parts availability and response times may vary according to country. You may be responsible for shipping and handling charges if the Apple Product cannot be serviced in the country it is in. If you seek service in a country that is not the country of purchase, you will comply with all applicable import and export laws and regulations and be responsible for all custom duties, V.A.T. and other associated taxes and charges. For international service, Apple may repair or replace Apple Products and parts with comparable Apple Products and parts that comply with local standards.