Not really. Not as much as you think they are (pointing at Americans here). We have survived, nay thrived without having what you'd call amiable relations for the better part of our existence. Pakistan does not need India, but, to great frustration of our friendly neighbor in the east, reverse is not true.
Pakistan lies at the cross roads of South Asia, Central Asia, Middle East and China, in arguably the most geo-strategically critical position second only to Turkey. At the core of emerging pillars of power and at the very point of concurrence of evolving trade lines. The geo-strategic location of Pakistan alone allows her to effectively curtail Indian designs of expanding its sphere of influence westward, paralyzing her ability to directly and deeply engage with their next door neighbors.
As India dreams to become super power, or even a middle power for that matter, it will need more than just a booming economy to win the title. She needs to be able to project power globally and construct a deeper relationship with culturally different and geographically far flung states. That, off-course, is unattainable as long as a nation of 20 million strong, having nuclear tipped missiles is standing in her way.
Pakistan on the other hand, has nothing of crucial importance to obtain from India except a few dozen trucks of potatoes/tomatoes which we seem to run out of every now and then. We have historically had very little trade or communication with countries located east of us, owing to our cultural, religious and collective economical interests being tethered to western direction.
So as much as i admire Americans selling this narrative of Indian importance to Pakistan, hoping it would convince us to stoop even lower, in trying to appease Hindu-national establishment of India (which is hell bent on provoking Pakistan through state-sponsored terrorism in Baluchistan and Karachi), I most certainly would contest its truthfulness. This statement is based upon assumptions that divorced from current ground realities.