No you cannot. Only on your home capital continent.
Well that's disappointing. I guess will need to create a special type of protectorate for India called 'princely state' or something to allow to call them into war if needed while still subject to your European nation, especially considering how valuable India are and also considering the 'divide and conquer' strategy that British historically used. They often employed armies of native states besides King's troops and Company troops in defending/expanding their empire in India.