Quite so. In reality, almost all of the Soviet nuclear missile subs were nearly continuously shadowed by American hunter killer subs, but the reverse wasn't true. In the event of an actual nuclear war very few of the Soviet missile boats would have survived, while almost all of America's would have.

Nevertheless, it turns out that land based ICBMs can also be made highly survivable so even given this any US/USSR exchange of nuclear weapons would have been devastating to both sides, regardless of how many subs survived.