No, any trademark registered in India will be valid only in India. However, some countries use the trademark filing in India as a basis for registering the trademark in their country
FAQ Group: Trademark Registration
Registered trademarks are valid for 10 years from the date of filing. The owner of the mark can file for renewal to keep the trademark protection current prior to the end of its validity.
Any word, name, device, label, numerals or a combination of colors that can be represented graphically can be registered as a trademark. The trademark to be registered must also be distinctive for the services or goods for which it is proposed to be registered.