They were operating normally boarded a contagious sailor and it was too late before a strict quarantine went into effect. If we are to believe what happened to the survivor cruise ship in season one and the flashback to Ramsey assuming command of his submarine happened to everybody. Except the few like the Russian admiral who was not locked out by security and secrecy.
It's not beyond the realm of the possible that at least one American sub was deployed with a clean crew when the outbreak ramped up (in fact, it's statistically likely). If so, if somebody knew about they would probably tell the sub to stay out and survive till things blew over, and things just never blew over. So the crew maybe surfacing intermittently hunting for food and trying to get news. Probably in the Pacific.
Anyway, could happen. We just have to see if the writers think of it.
Now as for the rest of the ships we have a broke destroyer after two torpedo near misses and a flooded magazine. Assuming the fleet wasn't all at sea, and we saw ships docked in Norfolk, it makes more sense to trade Nathan James in for another just as Starfleet had done with Enterprise and Defiant, rather then whoever survived trying to jury rig repairs. But they will try to repair her and she will be fine just like Voyager.
Hollywood logic: Name recognition beats common sense. They could easily transfer to a fully functioning Burke if one's available, but they've burned the Nathan James into our psyche's for two seasons now and they'll probably be leery about suddenly using the Oscar Austin or something...