The additional surface area added by extending the rear fuselage is essentially valueless for helping longitudinal stability. In terms of the longitudinal axis, you can almost disregard the aft fuselage - simplistically, you have a forward fuselage (longitudinally destabillising, but it doesn't lift too effectively), a wing (obviously a good source of lift!) and a tailplane (nice and stabilising). If you didn't need something to fasten the tail to, you wouldn't really need the aft fuselage.
Adding to the "tail arm" by increasing the distance from wing to tail makes the tail generally more effective in stabilising the aircraft and also more powerful as a control surface. Simplistically, a 10% increase in "tail arm" is worth the same as a 10% increase in tail area. Since it's usually easier to lengthen a bit of fuselage than redesign the whole tail, that's what people usually do.
As to what would it have done to the Spitfire. Made it a bit more stiff in pitch (higher frequency short period) and given a bit more pitch control power. All depending exactly where the cg was. Would have made the ground angle less nose up - might have been good or not, no clue about taildragger behaviour. They didn't do it, and it's a relatively simple mod, so they clearly didn't want to do it, and probably didn't see enough of a need to do it.