The answer is “YES,” if you believe the US declassified reports now available on Wikileaks. A classified cable generated on 2009-03-06 by US embassy in New Delhi states “Eventually, naval sources indicated, Cochin will seek to manufacture nuclear powered carriers.”
Cochin Shipyard Limited is currently building the first 37500-ton STOBAR indigenous aircraft carrier (IAC), now called Air Defence Ship (ADS). ADS (expected to be named INS Vikrant) is slated to replace the aging INS Viraat, and will, together with INS Vikramaditya (originally Russian Navy Admiral Gorshkov), form the core of the Indian naval fleet. The 260 meter long IAC, built in collaboration with Italy and Russia, will carry twelve MiG-29Ks, eight Tejas Light Combat Aircraft, and ten helicopters on its 2.5 acre flight deck and hangars. It will be manned by a crew of 160 officers, 1,400 sailors, and will be powered by four LM2500 gas turbines.
Indian designed nuclear submarine INS Arihant (S-73), (Earlier designation S2), is advertised to be powered with 80 MW pressurized water reactor with enriched uranium fuel. French aircraft carrier Charles de Gaulle (R91) with full load of 42,000 tonnes is powered by 2 × K15 pressurised water reactors (PWR), 150 MW each. It is unlikely that New Delhi will begin constructing a nuclear powered carrier in short or medium term as it will focus on completing the ADS. It is speculated that the S5 nuclear submarine, which is yet to get a go ahead for construction, may incorporate a more powerful reactor, possible of 150 MW class.
It might be possible that Cochin Shipyard can deliver a nuclear powered aircraft carrier by 2050.