Ooh so much pressure.....
Start with Pros: Ultimate power projection. We can not only threaten Mumbai but all the way down the eastern ghats. This is India's soft underbelly. They have no defensive weapons deployed and it is their strategic depth. By threatening that, you push them to re allocate their assets relieving pressure on the border or they spend a whole lot more to put AD assets in mumbai, chennai etc.
Cons: Obviously a whole lotta expensive to operate and have a dedicated Task force with Area Defense destroyers, forward screening submarines and other support ships.
I must say, I have never given much thought to having a blue water navy just because of the dire economic situation we always seem to find ourselves. It does opens up a chess game between bigger powers. If US et al are trying to prop up India as a counter weight to China. China can pre-empt that by "propping" up Pakistan and trip up India. In that case fiscal issues go out of the window.
China can "loan" us the vessel just like INS Chakra and the new Akula SSN Russia loaned India.
Ideally I would like PLAN A/C somewhere off the coast of Yemen launch PAF aircraft. They interdict deep south and return to a land base. No fuss no muss. You can say, they did buddy refuelling and the strike was launched from a secret "Shangrila" base