Sure, when the reactor in question is operated using 1950s-era dials and valves and shit! But you'll have to do more to convince me that what you say still holds true today, with modern computer control.
The problem becomes that you don't want it anywhere near a port in case it goes wrong. Sure, the USN claims they've never lost one of their reactors, let's say that's true for just a moment. Russia has lost some. It's not outside the realm of possibility. And while a computer can in theory substitute for a highly trained crew, in practice uh no, and also no. Not in this case. So basically, it's a useless idea.
We need future-technology electric power storage to really solve this problem, or future-tech materials technology so that we could for example build submerged tube trains, or a chain that would pull container ships along, etc etc. Barring that, we could be producing biodiesel from algae and using that to run ships. NOx goes up a bit, CO2 goes way down, so does soot — as compared to #2 diesel, let alone marine diesel, double extra let alone bunker fuel.