That sounds something like Cavorite from Wells' FIRST MEN IN THE MOON.
Admittedly it does, but so do the enigmatic dilithium crystals or - for comparison - AVATAR's unobtainium.
In his main thread blssdwlf
has presented substantial evidence that the Enterprise
is capable of re-energizing itself amidst classic particle exhaust propulsion principles (impulse drive).
Even if the weight of the ship mentioned by Scotty in "Mudd's Women" were only attributed to the bulk of impulse fuel and assuming they use fusion "rockets" they'd still require more fuel for exhaust particles than what ramjet or ramscoop technology would probably gather to get to Delta Vega.
Of course, if the ship were propelled by natural gamma radiation (like wind drives a sailing vessel) you'd have more solutions than technical obstacles to overcome, IMHO.
It's all highly exotic stuff but still one might want to examine which exotic approach is the least incredible one.