A couple assumptions there. One is that the CAP over Normandy was static in deployment of numbers. Actually that depended on German activity. Tho there were some attempts at improvements the Luftwaffes signals security was poor right to the end. Between excessive aircraft transmissions, sloppy use of tactical codes or security measures, traffic analysis of tactical transmissions, and longer term information from Enigma decrypts (the Luftwaffe was still using many older three rotor models from 1939-41), the Allied fighter command were able to anticipate on short notice the enemy air activity. Then there was observation by the French and Belgian underground of the forward airfields, near constant Allied air observation, and long range radar observation. I am more familiar how this played on in the Med in 1943, but as early as March 43 the air defense cmd in Tunisia were able to identify the oncoming air activity and counter surge fighter groups. Warning orders went out the the stand by fighter groups, often before the Axis groups were formed over the Italian airfields. By the time the Axis bomber or transport groups approached Arica the squadron size CAP units had been reinforced to multi group intercept formations, arrayed to intercept from multiple directions and altitudes.
This overwhelming intercept capability is why the Germans ceased any significant efforts at daylight bombing over Britain, and over Normandy in June 1944. From mid June night attacks became the norm for the Lufwaffe in attacking the lodgment and fleet. That reduced the combat losses significantly, but ran the operating losses up due to lack of training for night ops,. It also cut the effectiveness of the bomber attacks for the same reason, few veteran air crew remained, and the rookies training for night navigation and bombing was grossly insufficient.
A related problem was the Allied naives were authorized to use the VT type proximity fuzes. The optimal altitude of night attacks with the Luftwaffes equipment and training put the aircraft well within the maximum effectiveness zone for the naval AA ammunition with the VT fuzes. Between the radar direction of the ships batteries, and the proximity fuzes the bombers may as well have been attacking in daylight. I am unsure when the AA Artillery ashore were authorized the VT fuzes. They did have a fair amount of radar directed weapons, and sufficient ammunition. Attacking the lodgementfrom mid June, even at night was still at a noticeable combat loss of machines and air crew.
The CAP was flxible within certain parameters, some artificial like acceptance of risk and others real such as the limit on aircraft with the range to conduct a CAP over Normandy and the limitation of sortie generation. So while say 500 aircraft is an average there might be 600 on station at dawn and dusk and 400 for most of the rest of the day, or with a plane able to fly 6 sorties in 5 days some days they might get 1000 fighters on station for the dawn patrol or whatever. But that's it, they're not getting 3000 fighters over Normandy simply because there are 12,000 combat aircraft in Britain.
That said, Germany having 600 or whatever aircraft rather than 300 available over Normandy is going to provide only an incremental improvement, but they will provide an incremental improvement.