Yup, it sounds like low voltage has upset the computer. In 'limp' mode, the
is not really making its best efforts to run the engine efficiently. It's just trying to keep it going without damaging it.
Theoretically, a weak battery could increase fuel consumption by increasing the load on the alternator. The alternator senses the voltage of the battery and varies its output accordingly. With a fully charged battery, it will practically free-wheel, but with one that regularly drains, the alternator will take a lot more effort to turn, which will sap engine power and use more fuel.
A 120 amp alternator running at maximum output will draw 1.44kW of mechanical energy from the engine. If Wikipedia is correct (and bear in mind that it occasionally isn't) then internal combustion engines are still roughly only 20% efficient in converting fuel energy into mechanical energy, so that's 7.2Kw of fuel energy going in to produce 1.44kW of electricity coming out. A litre of diesel contains 9.7kW of energy.
The upshot of this? A bad battery (or any other heavy electrical drain) could, in theory, cost you nearly a litre of extra fuel for every hour of driving. Though in reality, if you were pushing that much energy into a battery that wasn't storing it, I'd expect something to either melt or explode.