Actual former XO of an Ohio class SSBN (USS Florida SSBN-728) then CO of a Los Angeles-class SSN (USS Indianapolis SSN-697), then commodore of an SSN squadron, answering. In other words, someone who has fought both classes of ship and knows what he is talking about.
Short answer: no.
Reason: maneuverability. Doesn’t matter what weapons you carry, if you can’t turn the ship in time to attack or evade, you are dead. Think of an F/A-18 engaged in a dogfight with a B-2. Even if the B-2 carried air-to-air missiles, it’s not gonna prevail.
I used to joke with my crew on the Trident: “Put the rudder over. I’m going to take a nap. Wake me up when we are on course.”
On the Ohio-class we were required to conduct ASW missions as part of our Tactical Readiness Evaluation (TRE), but we all knew this was for self-defense only. No commodore or admiral in their right mind would send a Trident out to hunt/kill an SSN.
