...if I was to fit a Corsa GSi gearbox to my car, would acceleration be improved and have a quicker 1/4 mile time?

My car is a 2000 Sxi Corsa B. It has had a 1.6 16v engine from a Sport fitted along with cams and throttle bodies etc.. but it is still got the original gearbox that came with the car when it was a 1.2 16v.

I don't know alot about ratios etc.. but am I right in thinking that the ratios are closer on the Gsi gearbox than the one I have now therefore giving me better acceleration times and 1/4 mile.

Any help much appreciated.