Are we assuming the objects retain form? If I smash two iron cubes together and apply enough gravity, eventually I'll get fusion of the atom cores. As the highly-compressed charged particles start to collide more-and-more, some will repel, some will fuse.

As long as the 2nd law is in play, I could see the two objects as being passed through each other. One side you have particlesA[cub1_particles, new_fusion_particles] and on the other side you have particlesB[cube2_particles, new_fusion_particles]. Both of these would sum to the same thermodynamic energy of [cube1, cube2].

Right?

To the size of their core, sure. But a collision happens way before the atom cores are close to eachother, as you already mentioned. Therefore it does not compare as an analogue.

Additionally, the densities of the systems are also very different (not in absolute terms of course)

Electromagnetism is some 40 orders of magnitude stronger than gravity. Also gravity only attracts, it doesn't repel like 2 atoms approaching each other. So it is really quite different.