This doesn't eliminate the tail (we still have to deliver ammunition, lubricating oil, food etc. to the fleet) and it doesn't eliminate replenishment at sea (we still have to get that stuff from supply vehicles to ships), but it does lighten the supply load and create more military options.
Lots of people killed by IEDs on long supply lines in Afghanistan is an extreme example of the human and military costs. Some of those died to fuel A/C for uninsulated tents... madness.
1) uranium -> nuclear power -> expensive synthesis -> local transport -> fuel
2) uranium -> nuclear power -> transmission lines -> charging batteries
3) crude oil -> refinement -> transport -> fuel
EDIT: Found a reference from another comment: http://en.wikipedia.org/wiki/Fischer%E2%80%93Tropsch_process... It says that the input energy is 2-4 times the stored energy for synthesized hydrocarbon fuel.
Instead of the energy system, consider the cost of military supply lines. There's more than the financial cost of delivery; long supply lines are vulnerable to attack and disruption. You don't need to imagine an example: consider IEDs in Afghanistan. Many of those were trucks delivering food and fuel to bases. Efficiency (i.e. insulating tents so less fuel is needed for A/C) results in less deliveries and less deaths.
The same principle applies at sea. Oil ships are a vulnerability and another thing to plan, as well as a major cost that can be more important than the energy efficiency issues.
