Yes, if the 'drone' is in the form of a USN Virginia class submarine that just sent a couple of MK48 ADCAP Mod 7 CBASS to break the back of the ship. However, if you mean a UCAV somehow managing to fly within range and drop ordnance on the ship that is a strong 'no.'
For two or three Drones to sink a Kirov they would also have to be able to sink a Tico or an Arleigh Burke. If you don't think that is possible then it will be just as impossible for a UCAV to do the same to a Kirov. For one I doubt it would be able to penetrate the air kill zone of the S-300 complex on the ship, and even if it did (say it is some super-stealthy vaporware) there is nothing current drones carry that can sink the world's largest combat ships (that are not aircraft carriers). The purpose of the Kirovs in Soviet cold War doctrine was to survive long enough to launch their nuclear-tipped Granits against US aircraft carriers. Now, the length of time they would survive was VERY limited (as was the case of every single sea-surface platform, from Soviet Kirovs to USN Carriers, if the Cold War ever went hot), but the Soviets tried to push that survival time a bit by basically making the thing into the world's largest anti-aircraft and anti-sub platform (136 SAMs and 102 sub-rocs). All to ensure it would have an opportunity to fire at least some of its 12 Granits. A UCAV wouldn't make it close, and even if it did there is nothing it would be able to do.