NiHaoMike: this has been done successfully already.
GasSavers member Brock saw a 5-7% increase in fuel efficiency even with this inefficient setup: He put two 6v golf cart batteries in his Jetta (in addition to the OEM battery), plus a DC/AC inverter connected to a 55A charger (to the OEM battery) which would keep system voltage at 14.4v.
He "manually" removed the alternator load from the engine by pulling its main fuse. (That way he could put it back in when his wife drove the car, so she wouldn't have to worry about monitoring the "boost pack" voltage.)
Details here:
Plug-in Blackfly: going alternator optional nets +10% mpg - MetroMPG.com ... near the bottom of the page.
The caveat in this approach is that batteries are consumable items. You'll save energy doing this, but without a cheap source of batteries (or unless fuel is far more expensive), you probably won't save money.
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Even if it did work you still have the same problem of an electric car( your using energy from a power plant instead of gasoline )
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It's not necessarily a
problem - power plants (even coal fired ones) generate power more efficiently than gasoline engines, so the net energy use is lower. Also, many people have access to renewable (clean) electricity generation so net pollution is lower too.