Sanskrit is one of the oldest written Indo-European languages, and I would like to know about its intelligibility with PIE. It was spoken starting around 1500 BCE, and Proto Indo European was spoken around 3500 BCE. For some context regarding similar timespan, I asked my dad if he ever heard Latin and how much he understood because he speaks Spanish as well as English. He said he heard it in church and understood it a little. That is what my guess is: a little bit, but not much. I’d probably say more than my dad did because Spanish doesn’t have cases and Latin does. Sanskrit has all 8 cases.
It is extremely unlikely that reconstructed PIE would be intelligible to a speaker of Sanskrit, but we can't know for sure since there aren't any native speakers of either language to do the test with. Testing with "preserved" languages like Latin, Ge'ez, Old Church Slavic is not a good test, especially Latin where many people have actually studied Latin. On phonological grounds, the divergence of presumed PIE and Vedic is rather substantial (substantial change in consonants via loss of laryngeals, labio-velars, change of palatals) plus a very different vowel system. The Sanskrit-PIE relation is more analogous to the Proto-Bantu to Shona difference... and Shona speakers cannot understand Venda, which is a very close relative within Bantu (and, they have no contact-based reason to be familiar with Venda). Phonological dissimilarity is an absolute barrier to comprehension, it doesn't matter if the case endings are very similar.
The infamous William Jones did not even see that Hindi was derived from Sanskrit, so, considering the immense number of changes of all kinds that separate Old Indian from PIE, it is highly dubious that a speaker of Old Indian would understand even a word of PIE. I think (s)he would not even be able to perceive Old Indian is derived from PIE.
A speaker of Ancient Greek and Latin might understand a number of PIE words as the phonology is more conservative in Greek and Latin.