12V battery TWIZY is it OK if I

Ok EV folks!!!
Question: the Twizy has a normal 12v battery right? I guess it’s a standard lead acid or anyway a heavy one.
What about If we replace it with something like the on the screenshot? It’s lighter and powerful enough it should help to increase milage as well since the traction battery wouldn’t get affected for headlights and other energy discharges right?

Might add upto 1/4 mile if all electrics were in use.

You would do better using supercapacitors, instant charge and half the price.