There was no Aryan ivasion. It was the creation of the bigoted british historians. These bigot did not want to believe that the highly sophisticated Hindu vedic philosophy could not have been the creation of the 'lowly' natives. Hence they came up with the theory that Aryans from souther europe invaded India with and converted the natives to the vedic philosophy.
The fact is that Indian vedic philosophy originated in India and embraced and accomodated native ideas. There never was any clear division of Dravidian and Aryan BS before the British.
If you look at the Sinhalese peopple, they resemble the people of southern India more closely. However, their language and culture is highly sanscritised. You can see that in their names even. SL is a good proof that there never was a distinct and separate Dravidian or Aryan culture or religions. Just that some regional practices were different.
You will see the same trend in Karnataka, Kerala and Andhrapredesh.