Call me skeptical. Using a ballistic missile to track and hit a moving target seems like a task out of their reach. The weapon would need some sort of external source to update the trajectory.....perhaps a satellite, land based, or sea based system. In a conflict, that would be the weak point and the first thing to go.
Inertial guidance as a stand alone guidance system is pretty accurate.
With an initial estimate within a hundred miles or so, finding a flat metal flight deck on water shouldn't be that hard. The rest is software.