The navy has plenty of nuclear carriers and submarines operating by splitting atoms instead of combining them. If ever fusion reactors on land start generating a great deal more energy than is put into them to get fusion started, could the technology by scaled down to fit inside ship hulls or submarine hulls and provide nuclear fusion marine propulsion to replace fission?
Nobody knows.
Because we don’t have a functioning fusion reactor yet. One could make educated guesses based on how scalable current designs are. But since zero of those current designs are anywhere close to working, you’d be extrapolating from near zero data.
Come back and ask again after we have working fusion reactors.
How long will that be?
Its been 10 more years down the road for something like over 50 years now.
We may as well ask which sort of Galleon -Wikipedia is the best aircraft.
A working fusion reactor is ten years away. Has been for half a century
Rather like Unix replacing Windows
Ten years is an underestimate. Usually it has been thirty years in the future. Always has been, always will be.
A few of the fusion startups are claiming reactor designs that are very small. Easily ship fit size. Of course they don’t actually work. But some seem to have burnt though a quite a lot of investors money. Not quite fusion, but someone is being kept warm and happy.
The technologies that might plausibly give us a continuously-operating, energy positive reactor will likely be too big, heavy and complex. But of course, as it’s still WIP, no-one knows for sure.
As a slight aside / hijack, the temperatures and pressures required to get nuclei to fuse is a good illustration IMO of how much stronger the other physical forces are to gravity. Even the sun’s tremendous mass, resulting in incredible pressures on the smallest nuclei possible…can’t quite get them to fuse. It needs quantum tunneling to get over the remaining energy hump.
Any heat source can be made into a naval propulsion source. The question is purely whether it will ever be possible to have a small enough fusion plant to put on a ship.
Some ships are pretty big, though. Even without knowing how large a hypothetical fusion plant would be, it’s hard to imagine it being too big to fit on an aircraft carrier.
Completely? That’ll probably never happen. But I’m pretty sure that the number of Unix devices in use passed up Windows years ago. Consider that MacOS, IOS, Android, and ChromeOS are all Unix.
Well, a friend in the Princeton physics department once said he believes the only practical way to contain nuclear fusion is with gravity. That reactor won’t fit on any ship. 
It won’t fit on an onshore power plant, either, though. And if you’re talking about the power plant just using collectors for the power, that was the primary propulsion source for ships for millennia: They just figured out a way to use the planet’s entire atmosphere as their collector.
Yes, there’s a real chance that we will never have a practical on-shore fusion power plant. That was my point.
And obviously, we use lots of fusion power indirectly: through burning wood, coal, etc., via wind, via dams, and via solar panels. Probably someone else I’m missing, too.
In a way, fission power is also (indirectly) stellar fusion, because uranium and plutonium, like all elements heavier than helium, were forged within stars of the distant past via stellar nucleosynthesis.
Very explodey stars, perhaps.