Main propulsion on a Kirov is steam turbine. It also has turbogenerators and GT generators. Perhaps it may have a diesel generator, but that would be good only for emergency lighting.Actually, even if reactors break down, the auxiliary diesel plant will get BCGN home.
Good training for them and a chance to show those long range AD missiles! Perhaps Chavez will ask for S-300!
No steam, no shaft, . . . it gets towed.