Certainly yes (Chandragupta), and not much if at all (Ashoka). Bear in mind that what with ancient communication systems, people only knew what was close and immediate to them, or what was reported by writers whose work got widely distributed.
After Alexander's death the most prominent figure in Hellenistic-Indian relations is Megasthenes, who was a close friend of Seleukos Nikator, and acted as Seleukos' ambassador to Chandragupta's court in Pataliputra. Megasthenes wrote a work called Indika, apparently a kind of ethnography, which is lost but which was evidently influential as a number of Greek sources refer to it. The New Jacoby editor comments that the surviving fragments suggest a political world-view informed more by Aristotle and the era of Alexander than by the era of the successors, so he may have written it before his stint as ambassador. The Indika didn't survive long in its own right: Strabo, writing about India in the 2nd century AD, relied on Eratosthenes rather than directly on Megasthenes. There are a few other notable names too: Nearchos, another contemporary of Alexander, sailed around the coast of India (we don't know how far); and Ptolemy Philadelphos sent one Dionysios on an exploratory and ambassadorial mission to "(one of) the kings of India".
It is probably thanks to Megasthenes that Chandragupta was known to Greek writers as Androkottos, or in Arrian, Sandrokottos. (If any Roman writers ever wrote about him, to them he would have been (S)androcottus). The sound shifts from Chandragupta to (S)androkottos are not very surprising: Greek very often drops initial s-, and k for g is just a matter of not voicing the consonant.
From the fragments surrounding Megasthenes we hear that there were at least two successive Seleucid ambassadors to the court at Pataliputra: Megasthenes during Chandragupta's reign, and Deiomachos during the reign of "his son Amitrochates", who must be Bindusara (though in his case it's a lot harder to tell just from looking the names). We also hear that they took measurements of the latitude in India for cartographical purposes. Plutarch, Life of Alexander 62.2, reports a story that Chandragupta gave a present of 500 elephants to Seleukos, and also mentions how Chandragupta "overthrew all India" with an army of 600,000 men.
Ashoka, by contrast, is not reported on in any Greco-Roman writers. The stuff we hear about him in Greek comes from Ashoka himself: he erected a number of inscriptions in Greek, clearly targetted at the Hellenistic populace. The most important one is a bilingual inscription at Kandahar, in Aramaic and Greek. Here it is as quoted by Fergus Millar, in Rome, the Greek World, and the East (2002) vol. 1 p. 30:
When ten years had been fulfilled, Piodasses ["he of benevolent countenance"] demonstrated piety before men, and from that time on has made men more pious, and all has prospered throughout the land. For the king abstains from (eating) living things, and other men - even such as are the king's hunters or fishermen - have abandoned the chase. And if any are lacking in self-control, they have left off their excesses so far as they can. Moreover they are obedient each to their father and mother, and to the elders, to an extent greater than previously. For the future, acting according to all these principles, they will live more agreeably and better.
The moral sentiments expressed here are not typical Alexander-style propaganda, but are of course a reflection of Ashoka's attempt to convert everyone in sight to Buddhism. The fact that Ashoka felt it necessary to raise an inscription in two western languages suggests a great deal of interaction between west and east; it's unfortunate that we don't have any transmitted testimony of how this interaction worked in his time.
Nearly all of the material I've mentioned here comes directly or indirectly from the New Jacoby article on Megasthenes, BNJ 715. If you have access to it, that'd be the best place to go for further details.