Presumably the effect would be less than by putting extra tanks behind the pilot, which are even further aft than the historical Spitfire radiator location!
Sure, I'm not suggesting that Supermarine should have just winged it. Obviously any changes and the implications thereof would need to be carefully calculated and tested.
(Another thing is that if the Spit with a ventral radiator like
S
spicmart
and you propose, is that you can no longer put a drop tank or bomb on the centerline. So these external stores would have to be mounted on wing hardpoints. And by moving the radiator behind the pilot would also change the CG compared to underwing radiators, probably the wing would need to be mounted further aft on the fuselage. etc. etc.)