The conditions for propagating fusion burn were not well understood at the time, as one might expect, but we know them pretty well now. A key paper on the topic is this one:
Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications
The key concept here is that the fusion propagation velocity is a function of density - simply because the alphas don't have to go as far before hitting some fuel. But even at ridiculous density, the fuel mass is disassembling even faster, and so there's a race while you try to get as much fusion as possible in the short time when the fuel is "dwelling" at maximum density.
For instance, in NIF, the density is about 100 times that of lead, and assuming a hot spot, the physical expansion of the fuel is still faster than the fusion propagation. This is why it is so hard to use ICF for power generation, as the fuel tends to blow itself apart too rapidly.
I am not familiar with Jupiter's lower-layer conditions, but I don't believe they reach this sort of density. That suggests it will not be possible for it to maintain a propagating burn, and that any fusion events that occur would cause the local area to essentially blow apart.
UPDATE: a little googling shows the conditions on Jupiter were much less extreme than I thought, about 300 K and 10 atm, so the fusion rate will be tiny and definitely not sustain ignition.
