Yes, India has little need for local defense as the Indian Ocean is basically an Imperial Lake. All access points are covered by Empire bases. Germany did have pre-war plans to use the Pacific Squadron on raids around Australia to draw off RN strength from the North Sea but these plans were binned once the RAN was established with HMAS Australia as a core. The Dreadnought Armoured Cruiser was the antidote to the fast raider (converted liner) that the German's were known to be planning - the sheds housing the guns at Kiel had the liner's name painted over the door.here's two key concepts when it comes to dominion defense.
1. Local defense.
2. Imperial defense.
I certainly agree that a battlecruiser would do better for contribution towards imperial defense however I believe that a battlecruiser might be overkill for local defense. If we were to judge the threats believed likely in the Indian Ocean in the case of a major war we could rank the threats to be 1. Auxiliary cruisers (very likely) 2. Protected cruisers (somewhat likely) 3. Armoured Cruiser (unlikely). The idea of enemy battlecruisers in theater isn't even being considered. Von Der Tann (Germany's first battlecruiser) hasn't even been laid down yet. If they looked at a 'flagship' a year or two later they may have decided battlecruiser. I don't know.
It's also less likely that the Royal Navy will be calling for a "second class cruiser" or "armoured cruiser" to deploy to home waters as soon as war breaks out.
The economy of this British India is somewhat stronger than our time line but at the same time it can't go buying a Battlesquadron for the Royal Navy.
For another thing a battlecruiser is limited to Ceylon for drydock in the Indian Ocean (with Singapore and Alexandria as options outside the immediate area).
One of the drivers for this could be nationalism in that Japan has just earned the respect of the world with the success of their navy. India could utilise the same idea. In this case large units will provide the necessary prestige. This is also coinciding with Fisher's first stint at the Admiralty, there was very much aversion to building '2nd rate' or '3rd rate' ships when time would provide them anyway. Colonies had been contributing cash to support local RN units of poor quality (these 2nd and 3rd rate ships). Natal had just taken their subsidy and put it towards the gift of the Warrior Class Armoured Cruiser HMS Natal. India could perhaps do something similar in the initial step and then have these gift ships signed over to a fledgling RIN, perhaps 3 more Minotaurs, followed by 2 Indefatigables. A RIN may see 2 Fleet Units, one for the Med and one for the China Station as serving their local needs rather than contributing to North Sea strength.