If you're English, your fighter can't hold enough ammo to make a significant impact on the German offensive. We're talking about days where hundreds of planes are being shot down in the course of an afternoon.

If you're German/Italian your fighter as well, can't hold enough ammo to make a difference or your bomber can't hold enough bombs or make enough sorties a day to do the same.

Look at Erich Hartmann! The guy shot down 352 aircraft on the Russian front. The Germans has ton's of 100+ aces, and they still lost the war. For every plane you shoot down, there is a an ace on the other side to do just the same. That's why you'll never see a difference.

I could see something along the lines of you being singled out by the enemy once your kill count has reached ~20 or so.

(enemy radio chatter) "There's that devil that took out Fritz/James yesterday! He's the one that's been swatting all our comrades/blokes out of the sky. Registration number 123. . . Swarm him!"

That could be sort of cool! Not something like, "The Italians have pulled out of the conflict after you downed 35 of their pasta-planes into the drink. Good show!" Or something equally unrealistic like, "The Fuhrer has ordered operation Sea Lion to go ahead. Your efforts have single-handedly resulted in the RAF being crippled as a fighting force!"