If you have an 11.1V battery and it droops to say 8V at 100 amps, that big 1F capacitor will last:
11.1 - 8 = 1 x 100 x time.
Time = 31mS. That is getting to be a useful size now.
The energy is 1/2 x 1 x (11.1^2 - 8^2) = 29.6 Joules.
So caps rated at 100000uF (0.1F) and above are probably the range needed to do any good. Unfortunately, they are still going to be pretty big!
You also have to watch the ESR or internal capacitor resistance. Our guns are about 0.1 ohm so a 10 ohm ESR cap is worthless. But very large caps "should" have a low enough ESR.
In general, going to a better battery with maybe an extra cell is far easier.