India has been failing to industrialize for 30+ years. The real capital investment capability of westbloc is limited. They do not have the capability to prop up India without return indefinitely. Westbloc also will 100% be wary of creating a new true competitor in India because they're on guard now that China escaped their grasp. That is why all of India's real software giants like Flipkart are owned by westerners now.India is trying to capitalize on the West-China decoupling trend to position itself as the West's new manufacturing hub, so I'd say yes. India has good relations with all the developed world and wants to industrialize so India is not too desperate to better relations with China.
The smart play for China is to better relations with India and encourage India to compete in services rather than manufacturing. Keep in mind that just as the West runs a big merchandise trade deficit with China and wants to diversify to countries like India, China runs a big service deficit with the West and should diversity into countries like India. In this way, it would prevent India from becoming an industrial competitor, encourage more competition between India and the West, and gain more leverage over it and diversify from the West.
India's only hope of maintaining sovereignty is to balance between westbloc and eastbloc. Otherwise, it won't be leveraging westbloc to beat China, it would be being subsumed by westbloc as a colony again. I also believe that Indian leaders are smart enough to see this, which is why they're still working with Russia. Yet, as long as India works with Russia, westbloc will never trust them, and thus the likelihood of integration with westbloc becoming subjugation increases.