Likely, submarines are slow and quiet, and this would be very, very quiet given there wouldn't be pump noise to worry about. That's the big hurdle with the current subs, you have to circulate water in and out of the reactors to keep them cool, and for an attack sub, you don't have enough insulation/mass/space to keep them 100% quiet. The missile subs are much quieter, though, once you cook off a missile...well that's a very loud thing to do in a very quiet place.

There is still the problem of the rest of the sub's power needs. I can't imagine they're terribly efficient given they have a reactor available...