Well, Pali is a sort of standardised form of Middle Indo-Aryan, so, yes.
But you suggested there would be very little left. Yet the core of both Hindi & Urdu is (unsurprisingly) inherited from Vulgar Sanskrit>(some sort of) Prakrit>Apabhramśa>... , so it's rather a lot of vocabulary that's there.
For the more modern vocabulary issues (borrowings from Persian, Perso-Arabic, English, Portuguese etc.) in Hindi/Urdu, I would recommend the introduction to
(1) Christopher Shackle & Rupert Snell. 1990. Hindi and Urdu since 1800: a common reader. New Delhi: Heritage Publishers.
[which is actually now freely available online at https://repositories.lib.utexas.edu/handle/2152/46072 (had I known, I would have linked it earlier/higher in the thread, since it's very relevant) its bibliography is also good for further reading]
For the earlier development of modern Indo-Aryan languages from Sanskrit:
(2) Jules Bloch (ed. & translated by A. Master). 1965. Indo-Aryan from the Vedas to modern times. Paris: Adrien-Maisonneuve.
For a good general overall (including history and other things) to Indo-Aryan languages:
(3) Colin P. Masica. 1991. The Indo-Aryan languages. Cambridge: CUP.
In Hindi (modelled on S.K. Chatterjee's The Origin & Development of the Bengali language [written in English!]):
(4) Tiwari, U.N. 1961. हिंदी भाषा का उद्गम और विकास [hindī bhāṣā kā udgam aur vikās]. Prayag, Allahabad: Bharati Bhandar.
But you suggested there would be very little left. Yet the core of both Hindi & Urdu is (unsurprisingly) inherited from Vulgar Sanskrit>(some sort of) Prakrit>Apabhramśa>... , so it's rather a lot of vocabulary that's there.