Well, you basically have to script this mechanic, and it's not exactly simple to script, either.
Probably the best way is through a Built-In Hull Mod (that nobody else can use) that would implement the strategic effects of fuel use on CR (see Tow Cables for an example). I'm really not sure how hard that would be to write; I haven't explored using that code much.
In terms of balance, having that as their "thing" would be a pretty major buff in and of itself, since Fuel is cheap. They'd need some pretty major penalties to their combat stats or they'd have to be heavily penalized in terms of resource consumption (i.e., they're great if you're right next to a base with lots of Fuel, but they'd be terrible at chasing things).