parsifal
Colonel
Although not obviously relevant to the question of how the Allies would respond, it may be worth noting that large numbers of Me 262s could cause other problems for a Normandy invasion. Firstly, there won't be any great surprise as reconnaissance aircraft can watch the invasion force in harbour and as it assembles. Secondly, jets could be used (as I suspect Hitler intended) for skip bombing against the supply ships. I am not sure how much trouble that will cause or what losses the jets will suffer in such attacks. Bomb laden jets at low altitude can probably be caught by lucky piston engined fighters and the speed over the target will not make jets immune to flak although some of the guns may have problems following crossing targets.
in relation to your first point, highy unlikely, or extremely foolhardy if attempted. The germaans, like everyone, would be cautiousto place extremely secret and highly valuable jet techniologies in harms way over enemy teritory. by way of comparison, it was 5 months before the Meteor was cleared for service over europe, and even then only over or near allied controlledterritory. that was many months after the 262 had entered squadron service
In relation to your second point, fighter bombers were notoriously bad at hitting moving ships, they could do it,and they could even hit ships,but as a rule of thumb prop driven FBs were roughly half as accurate as dedicated Divebombers. Rocket firing FBs like the befighter had some success, but in order to improve accuracy, generally had to reduce speed. reduce speed inan aircraft like the me 262, and you are immediately in trouble. And I doubt the 262 could slow down enough to be effective in this role. The best FB in the anti-shipping role in my opinion wasthe fairey firefly. it was accurate for a number of reasons, but chief among was its patented youngman flaps, which allowed their deployment even in 90degree dives. it greatly increased the bombing accuracy. no other flap, including the junkers design could match its capability. but it would not be possible to safely use it in an enemy controlled airspace.
even in my era,when our F-111s were using all but stand off weaponary lke the harpoon, to achieve better accuracy, the sircraft had to reduce sped to subsonic. That was with computer assisted aiming....the 262 would be relying on los the same as other a/c of its era. becauseof it high minimum speeds, it would not be very accurate at all.
An Me262 carrying boms would have to suffer some penalties in speed andother performance, and make it quite vulnerable to alled air defences, both AA and airborne. I thinkn a 262 used as an anti-shipping weapon would have yielded virtually no results. with regard to flak,wwii era guns would have no problem tracking a jet travelling at subsonic speed. We were tracking A-4s at 500 knots using 4.5" guns and even Bofors in the 70's , so why all of a sudden would a 262 be immune???