I think it's very unlikely, that Dravidians lived anywhere north of Iran.. It may be possible, that in very prehistoric times some Albinoid Dravidians settled in those regions to escape the sun. We still have no real evidence for Dravidian being the mother of the Indo-European languages, but many scientist have come forth with such notions. This would be a breakthrough for the prehistoric department.
It is important to note, that the ancient peoples of Egypt and Near East had a very clear Dravidian appearance. There is sufficient evidence for it in Egypt, Sumer and Elam, such as simple wall paintings. Looking at this arts is like looking at my own people, but in different dresses. The ultimately Dravidian ancestry of the white people is the most favoured one by genetics and linguistics.