No, fusion occurs due to interactions between Deuterium atoms over distance scales that require that the atoms are in extremely close contact. Therefore, there is no room for any intervening atoms, therefore no medium is present.
Maybe this is where quantum theory meets physical world. The atoms are "forced" together, serially, like in a vise, under such pressure that they combine into a helium atom and release energy as heat, only under a controllable process that can be harvested. Maybe the palladium and zirconium dioxide act as the atomic "jaws" of the vise to produce this "fusion" slowly, instead of instantaneously in one "Big Bang"!............
About 1/3 of the way down there is a post (and related links) stating that the late Julian Schwinger had performed Quantum Mechanical calculations indicating that "cold fusion is possible because when deuterium atoms are trapped in a palladium lattice, their proximity allows for their quantum mechanical interactions to bypass the hot fusion requirement of high energy collisions.
As Schwinger was a Nobel Laureate and certified genius, that really got my attention.
Your thoughts?
Cheers!