India and China were the largest countries (or regions) of the world for most of the period from the fall of Rome through the early stages of industrialisation -- say the 17th century. But they lacked the global reach European nations established -- Portugal ("Bombay" comes from the Portuguese "Bom Bia", or "good harbour"), Spain, the Netherlands, and of course England.

What India and China will need to compete with the West is a large wealthy class. That's going to depend on both the absolute size of their economies (or their capabilities to extract wealth by other means), and the size and wealth of individual members of their wealthiest classes. China's economy is pulling even with that of the US, though how sustainably it can do so remains a question. It has over three times the population, though, so the mean wealth will be smaller.

What we're looking at though is the stratum of the ultra-rich. Here there's a fair argument that, say, China could produce more billionaires than the US, and if I'm remembering recent stats correctly, it's approaching that count. Again, though, that's somewhat shakey, and it helps to remember that such standings aren't based on liquid wealth (cash and equivalent holdings), but on the valuation of held assets. Should the Chinese or Indian economies collapse suddenly, those valuations will fall (of course, the same caveat applies in the US, UK, or EU).

I would think sufficient and reliable electrical power would be a prerequisite for that, and to my knowledge that isn't going to happen in India in the foreseeable future.