Short answer: Yes.
Longer answer: Well, essentially, my understanding of this is as follows: The Indo-Aryan languages can be divided into three stages, namely Old Indo-Aryan, Middle Indo-Aryan, and New Indo-Aryan. Middle Indo-Aryan is descended from Old Indo-Aryan; New Indo-Aryan is descended from Middle Indo-Aryan. Thus, all Indo-Aryan languages are ultimately descended from Old Indo-Aryan, and specifically from
Vedic Sanskrit, the language in which the
Vedas were orally preserved for hundreds of years before finally being written down. However, "Sanskrit" is normally used in the linguistic literature to mean not this but Classical Sanskrit, which basically started out as a written variant of Vedic Sanskrit (making Classical Sanskrit also a variety of Old Indo-Aryan) but since then has been heavily influenced by other vernacular languages, much like Classical Latin. Vedic Sanskrit also split up into various dialects that became the Middle Indo-Aryan languages, which eventually evolved into the New Indo-Aryan languages. Prakrits are a subset of the Middle Indo-Aryan languages that were used for writing literature beginning with the Edicts of Ashoka; many, but not all, New Indo-Aryan languages are descended from Prakrits.