Well, depending on how you define it. See exchange below with a reader. The relationship between Indian civilization and Islam is long and fraught (dating back to the Umayyad conquest of Sindh). Between the 16th and 19th centuries the Mughals created a civilization in the Indian subcontinent which synthesized many different strands. Even those Muslims who wish to reiterate their relationship to the peoples of West Asia by the 19th and 20th centuries were part of an Indian Muslim culture, which had co-mingled with the indigenous substrate.
That being said, during the 16th and 17th centuries I would argue that on the spectrum of indigenous vs. alien the Mughal elite tended more toward the alien side. They were in India, but not of India. Obviously this can not be taken too far. But I would offer the following point: India was a land of opportunity for Persian administrators and Turkic soldiers. Though certain high caste Hindus (and later on elite Indian Muslims) entered the service of the Mughals, they were initially outnumbered, and often given less prestige and lower fiscal rewards. This constant infusion of foreign Muslims into the elite meant that the process of indigenization could be halted and even reversed. Three of Shah Jahan’s grandparents were Rajputs. But he married a woman of Persian background, redoubling the West Asian cast to the family’s background. This might explain why they persisted in using their wealth in repeated attempts to conquer Kandahar.