Theemile wrote:No… it wouldn’t.
One of the first emisisons of the nuclear event (but not the first) is a neutron wave, and water is a neutron absorber – or more importantly – the hydrogen in it is. The neutron absorption has the effect of turning said hydrogen into deuterium and tritium. (And all water contains a small fraction of deuterium and tritium in its natural state.
The heavy Hydrogen isotopes add to a nuclear explosion when injected into an atomic pit and the pressures created in the pit cause them to fuse. Depending on the amount injected and timing – this either enhances the atomic explosion by the injection of more spare neutrons into the fissile mass (Uranium or Plutonium) increasing the reaction, or creates a second, fusion explosion when the force of the (nearby) fission explosion compresses the deuterium and tritium.
The Deuterium and Tritium in the water is outside the nuclear events and will never achieve the temperatures and pressures necessary to fuse. AS I said upthread, timing and position in a nuclear device are, and have to be, insanely accurate.
You seem to be talking about a boosted fission design where some fusion fuel is injected into the pit of the fission bomb. But that's still the primary for a thermonuclear bomb. The design that, as far as I know, all current thermonuclear bombs uses is the Teller–Ulam configuration where there's a secondary, with the fusion fuel sitting off to the side of the primary boosted fission core. See
https://en.wikipedia.org/wiki/Thermonuclear_weaponThe radiation from the explosion of the primary interacts with the material wrapped around the secondary's fusion fuel to initiate the larger secondary fusion explosion.
That same radiation would be slamming into the surrounding water; however I think without the special wrapping material it won't undergo the conversion necessary to trigger any appreciable amount of extra fusion.
So ultimately I think you're right, detonating a fusion bomb underwater isn't going to get any noticeable extra fusion. But it's not because the water isn't inside the primary core; it's because it's not wrapped in the materials necessary for the secondary stage's fusion material to get ignited by the radiation wave from the primary core's detonation.