I'm actually doing my dissertation on this period, so I'll try to answer your question as best as I can! I will draw on the archaeology and history of both Central and South Asia, as they both serve as examples of a similar process of Hellenization, or rather, cultural amalgamation.

To address the first claim as well as to give some historical context, Central Asia saw a massive influx of immigration from the Western Greek world as a result of Alexander's invasion of Bactria and the Greco-Indus, regions in which he founded many cities, notably Alexandrias, that would come to greatly prosper (with some serving as the foundations of modern cities). As Macedonian and Greek migrants, known to the local Buddhist populations as yavanas (deriving from ionian) settled in these areas, they surely would have left some biological traces in the ancestry of the native peoples, most prominently displayed in more extreme cases of isolated communities retaining distinct features such as blue eyes and fairer skin, as you have suggested. To me, this is a relatively minor feature of the broad and diverse cultural exchanges that occurred over the centuries of Greek rule on the eastern frontier of the Hellenistic world. After the rise of the Successor kingdoms and the secession of the Greco-Bactrian kingdom from the Seleucid empire, the eastern frontier's connection to the Greek world was hindered, and over the centuries the ruling Greek elite would become a smaller and smaller minority, and their traditions would increasingly adapt to those of the local population, forming a melting pot of art, architecture and religion, that would have a hand in shaping Central and South Asian material culture.

Many examples of clearly Hellenistic influenced art survives, notably from the region of Ghandara and its distinct form of Ghandaran art. Stupas from this region display Hellenistic scenes with common Greek motifs. Some depict clear Bacchanalian scenes of wine-drinking, men and women in Greek dress and chlamydes (a kind of Greek cloak), cupids, garlands and palatial scenes that borrow from Greek mythology. The first representations of Buddha in human form are thought to have been created as a result of Hellenistic cultural influence, and some stupas even depict Heracles as a Vajrapani or protector of Buddha.

Architecturally Greek buildings in major urban centres such as Ai-Khanoum (speculated to be Alexandra on the Oxus) show us the strong presence of Greek material culture in Central Asia immediately following its occupation by Greek settlers; yet as the Greco-Bactrian became increasingly isolated over the centuries, this material presence adapted more and more to local practices. An example of this are architecturally Greek temples with an inner layout of a Zoroastrian temple, or later Indo-Greek coins with Kharosthi (a script of Sanskrit) legends, and a Buddhist text (the Milindapanha) that describes a renowned Greek king (Menander I Soter) converting to Buddhism! Some suggest that over the centuries, the presence of Hellenic culture in Central and South Asia had diminished, with the yavanas eventually becoming an insignificant minority, yet the echoes of Greek influence in the history of these regions remind us of its persistence, which may have been facilitated by multiple preceding philhellenic dynasties (Kushan and Parthian). I suggest that the period of Hellenization seen in both Bactria and the Greco-Indus aided in shaping our modern conceptions of Central and South Asian culture, and that without such influence, modern Asian art, architecture and religion may have developed in a different way. By this assertion I do not mean to diminish the uniqueness and innovation of these distinctive parts Asiatic heritage, but merely to acknowledge the influence of Alexander's invasion, colonization, and the establishment of the Hellenistic dynasties as evident factors in the development of such a beautiful and diverse culture.

Sources:

Holt, F. L. (1999) Thundering Zeus: The Making of Hellenistic Bactria. University of California Press.

Samad, R. U. (2002) The Greeks in Ancient Pakistan. Karachi: Indus Publications.