Strangely, I could not find a single website run by the Indian government that could answer this question (please let me know if you do!). So I turned to my attention to Wikipedia and found the answer there:
As of now, India does not have an absentee ballot system. Section 19 of The Representation of the People Act (RPA)-1950 allows a person to register to vote if he or she is above 18 years of age and is an ‘ordinary resident’ of the residing constituency i.e. living at the current address for 6 months or longer. Section 20 of the above Act disqualifies a non-resident Indian (NRI) from getting his/her name registered in the electoral rolls. Consequently, it also prevents an NRI from casting his/her vote in elections to the Parliament and to the State Legislatures.Source Article: Absentee voting in the Indian elections
The Representation of the People (Amendment) 2006 Bill was introduced in the Parliament by Shri Hanraj Bharadwaj, Minister of Law and Justice during February 2006 with an objective to amend Section 20 of the RPA-1950 to enable NRIs to vote. Despite the report submitted by the Parliamentary Standing Committee two years ago, the Government has so far failed to act on the recommendations. The Bill was reintroduced in the 2008 budget session of the Parliament to the Lok Sabha. But no action taken once again.
Update: According to this, this and this article - it is now possible for NRIs to vote from outside India via "e-Ballot" or Proxy (nominating someone locally to vote on your behalf). So now the answer is - YES.