To use a fighter as a fighter-bomber when the strength of the fighter arm is inadequate to achieve air superiority is putting the cart before the horse.
Of course, the outcome of the war would not have been changed. The war was lost perhaps, when it was started. At least it was lost in the winter of '42, in Russia.
It is true to say that the first kill can influence the whole future career of a fighter pilot. Many to whom the first victory over the opponent has been long denied either by unfortunate circumstances or by bad luck can suffer from frustration or develop complexes they may never rid themselves of again.
As a fighter pilot I know from my own experiences how decisive surprise and luck can be for success, which in the long run comes only to the one who combines daring with cool thinking.
During the Battle of Britain the question "fighter or fighter-bomber?" had been decided once and for all: The fighter can only be used as a bomb carrier with lasting effect when sufficient air superiority has been won.