A large South Indian (Tamil) empire

[aware of emptiness]

(Inspired by the non-European colonial powers thread)
The Tamil Chola dynasty of South India in OTL was able to expand into Sri Lanka and South-East Asia (Indonesia, Malaysia) , and is largely responsible for Hindu influences in that region. The Cholas were seafaring, as far as I recall, and traded with the Abbasid Caliphate as well as China.
Could it have had the potiental to become an expansionistic empire?
I'm thinking, if they were able to spread more influence eastward, past Indo-China, or one of their sea boats made it to Papua New Guinea, Australia, or New Zealand, perhaps they could have founded a decent-sized colony in these places. The Australian and New Guinean indigenes, I think, are partially related to the Dravidians, so it would be interesting if such a contact was made, and they were able to spread their culture there. Seeing as there are lands farther east, would the Cholas be interested in expanding further?
Also, if they managed to venture westward, and settle Madagascar or even Southern Africa, could they colonized there too? If this possibility can be stretched even a bit further, would Polynesia or South America be out of the question.
Maybe this sounds a bit farfetched, but how plausible would a pan-Southern Hemisphere empire united culturally by South Indian (Tamil) influences? Once the actual dynasty at the homeland in South India falls, the Australia, New Guinea, Polynesia, South Africa, and parts of South America could all have descendents of the Cholas living amongst the natives and a syncretic culture could develop in each of these locations. It would be interesting, assuming the Age of Discovery for Europeans comes at the same time, how they would fare upon contact?

 

[Flocculencio]

The trouble was that the Chola, like most South Indian Empires (e.g. the Cheras and the Pandyas) followed traditional Hindu political theory which emphasised vassalage over direct rule. The Cholas and their ilk were primarily thalassocracies- concerned more with recieving tribute from vassals and securing trade routes than with ruling directly.

In OTL, as you say, there was a syncretic South Indian culture throughout SE Asia- it's just that it got fused with Islam, for the most part. If you could prevent Islam spreading into SE Asia it's cultural similarity to South India would be much more apparent.

 

[Tyr]

The trouble was that the Chola, like most South Indian Empires (e.g. the Cheras and the Pandyas) followed traditional Hindu political theory which emphasised vassalage over direct rule. The Cholas and their ilk were primarily thalassocracies- concerned more with recieving tribute from vassals and securing trade routes than with ruling directly.

In OTL, as you say, there was a syncretic South Indian culture throughout SE Asia- it's just that it got fused with Islam, for the most part. If you could prevent Islam spreading into SE Asia it's cultural similarity to South India would be much more apparent.

Well Britain preferred that sort of empire too and look where we got...

But overall I don't think its plausible still. They always loose me when it gets onto establishing colonies.