Probably not. They were designed to take out multi-ton supersonic cruise missiles so they need a larger warhead than would be required against drone swarms. Of course, since they're so large and capable they certainly could take down _a_ drone, and then it becomes a question of how large the incoming swarm is.
Now, if the incoming swarm is large enough, then either each drone carries a tiny amount of explosives, or each drone is large and expensive. The US Navy has been building ships to protect against mass swarms of incoming cruise missiles since about the 60s or so, so if the incoming drones are large enough then you could also use larger missiles against them and rely on the RAM only for whatever leaks through.
Now, if the incoming swarm is large enough, then either each drone carries a tiny amount of explosives, or each drone is large and expensive. The US Navy has been building ships to protect against mass swarms of incoming cruise missiles since about the 60s or so, so if the incoming drones are large enough then you could also use larger missiles against them and rely on the RAM only for whatever leaks through.