OOC:Actually, India did have an aircraft carrier, the INS Viraat, and its carrier aircraft are capable of carrying nuclear weapons. Of course, I doubt they actually have any.
The Viraat is a very old carrier (laid up during the Second World War) that should have been retired 40 years ago. Aside from that, its about the range of the planes on the ship; in this case the Sea harriers have to be 540nm away from the Chinese coast to be within combat range. Now that would mean India would send its lone carrier across the Indian Ocean pass the Malacca Strait, across the South China sea without refueling or restocking in what amounts to a suicide mission, they could theoretically do it, but it would make no logical sense.