It would have been common knowledge, or at least educated knowledge, but likely in a different sense than we understand their shared Indo-Iranian roots today.

It's nearly impossible to address anything about the Achaemenid period from the Indian perspective because there are simply no Indian sources. Though there are later records, especially in the Buddhist and Jain traditions, that refer to the same time period and even one grammatical text that is thought to be contemporary, none make any reference to a powerful state in the west. The closest we can find in the Indian sources are scattered references to the Kambojas, a people or kingdom located somewhere northwest of Gandara. Based on their name and description as horse riding herdsmen archers, modern scholars generally interpret this as an Iranian group of some kind. The same group is referenced as the Komedas in Greco-Roman sources.

In the Indian literature where they are mention, especially the Mahabarata, they are presented as part of the kshatriya varna. The 8th Century CE Skanda Purana refers to a Kamboja king who installed an image of Varahadeva, the boar avatar of Vishnu, on his throne. So these Kambojas were at least interpreted by the people of India as having a shared social and religious heritage. Interesting to that the boar was a symbol of the Zoroastrian divinity Bahram, patron of victory and righteous thought, and from the 4th-8th Centuries CE was a common motif among Sassanid Persian princes and nobles.

It is only slightly easier to take things from the Achaemenid viewpoint, but still easier, as they at least make direct references to other "Aryan" peoples in their inscriptions. The context for Achaemenid use of the word "Aryan" is always interesting. It is almost exclusively used in royal inscriptions with the phrase "I am [name, titles, genealogy], a Persian, son of a Persian, an Aryan, of Aryan stock." This phrase, in turn, is exclusively employed by Darius I and Xerxes in inscriptions where they reference rebellions in "Aryan" parts of the empire. Unfortunately, the exact contexts where it is used do not help us figure out if it was applied to India.

Darius refers to himself as an Aryan in the context of the DNa and DSe inscriptions, which both refer to the great rebellion at the start of his reign described in detail on the Behistun Inscription. This rebellion is said to include Sattagydia, part of the Indus Valley, but also many obviously Iranian regions. Xerxes says it in inscription XPh, also called the Daiva Inscription, which refers to a rebellion in an uspecified province, but I would argue that the description of "daiva worship" indicates somewhere Xerxes considered "Aryan." The Daiva were corrupted or false gods in Zoroastrian tradition, and this is apparently the sense employed by Xerxes.

The Achaemenids did not push their own religious beliefs on the people in the best documented parts of the empire, however the Behistun Inscription contains a unique condemnation of the Elamites and the Sakae/Scythians for not worshiping Ahura Mazda. This especially stands out at Behistun, where a dozen defeated enemies are listed and condemned for treason, but only those two are condemned on religious grounds. At first glance, it is difficult to find any connection between the ancient civilization of Elam and the horseback nomadic Scythians, but from an ancient Persian perspective, one connection may have been obvious. Both groups had strong cultural similarities to the Persians themselves. They shared gods, traditions, parts of their languages, and other customs.

Combined with Xerxes' destruction of a "daiva temple" in the same inscription where he too invokes his own Aryanism, it seems that there were additional religious expectations for fellow "Aryans." This is somewhat ironic in that no modern scholar would identify the Elamites as Indo-Iranian or otherwise "Aryan," but only because today that is a linguistic identity. This does not seem to have been the case in the ancient world.

By the criteria set out from those examples, it seems certain that the Persians would have recognized the people of northern India as Aryan in the same way they recognized the Scythians and Elamites. They too shared gods, customs, and language with the Persians, and probably significantly more than the Persians shared with Elam.

Now, whether that would have played out as cordially as portrayed in Creation, is hard to say, given Xerxes' destruction of the daiva temples in inscription XPh and the fact that the only Daivas named in any Zoroastrian literature all share names or titles with major Vedic Indian gods.