I think it's a slightly naive perception of growth, the reason Europe grew to dominans was the improvement of native production, if you look at the economies of the 17-19th their position was improved more through internal efficiency than through cash-mining of external sources, several of the powers which was came to dominans like Austria and Prussia lacked colonial empires, while both Netherlands, Portugal and Spain fell in the same periode. A richer India will result in more trade between Europe and India and as a result a richer Europe.
But I think you correct in that Britain will end up in a weaker position without India, but Europe as a whole; no.
You need money, in this era precious metals like silver and gold struck into coins, in order to invest in economic ventures (colony-founding, ship-building, goods-purchasing). With India independent it will be absorbing European coin and not giving it back. That means that coin will not be in circulation in Europe to be invested, which means the OTL investments that were made aren't, which means that Europe is less productive that it OTL would have been.
To give you a parallel situation from OTL: The British started selling opium in China in order to correct the trade in-balance that they had vis-a-vis China. Basically the British were paying coin for Chinese goods, and the Chinese didn't want any goods the British had. Opium corrected the in-balance, actually tipping it in Britain's favor, which set off the Opium War.
So, if Mughal India is independent and strong, Europe does not grow as fast, which will have serious knock-on effects for Europe. Specifically, the British did a LOT of the European empire-building, and the modern-world inventing, and they did with India as the money-producing engine of their Empire. Without that engine, the UK doesn't do what it did, and that causes all kinds of ripples.
Valdemar has it right. Besides, did we see Spain industrialize during the sixteenth and early seventeenth centuries, when they had the entire wealth of the Americas to exploit? Quite the opposite, IIRC.
Spain didn't industrialize, but the Dutch did with Spanish gold. If you don't have that Spanish gold in circulation in Europe, then you don't have the Dutch Golden Age and all of the opportunities that opened up to the rest of Europe. The Spanish spent significant amounts of their wealth paying various concerns in the Burgundian Inheritance for things like banking and manufactured goods. Those purchases couldn't have been made without the American gold. So no gold, no Golden Age, and history after that gets rippled.