So aside from all of the speculation and conjecture in this thread (not to mention the stuff that seems plain fabricated.) I did some searching on the matter, and it turns out that smoke was planned for, but not really required on D-Day.
"Brigadier G. H. Pennycock, director of chemical warfare for the British 21 Army Group, coordinated Allied smoke screening plans for the initial phase of the invasion. Colonel Coughlan, FUSA chemical officer, was in turn responsible for the operational plans for American forces. One problem which had been troubling First Army, the difficulty of landing the heavy M1 generators on the Normandy beaches, was eliminated almost on the eve of the assault with the arrival of the M2 generator which had a dry weight of only 172 pounds. Smoke troops received the first M2 on 13 May, 7 more on 24 May, So on the 28th, and 27 between that date and 3 June.4"
"Final plans for the use of large area smoke screens during the cross-Channel attack provided for smoke over the ports of England from which the invasion would be mounted and smoke over OMAHA and UTAH beaches in Normandy. In both cases the screens would be used as a means of concealing activity from German aircraft."
"The 79th and Both Smoke Generator Companies, with their men and M1 smoke generators aboard thirty of His Majesty's trawlers, on 9 June arrived off OMAHA Beach, where they served as the offshore element of the 23d Battalion smoke installation.
But they received no requests for smoke. The great storm of 18-21 June wrecked some of the trawlers and others returned to England for repair and refueling, never to return to OMAHA. Some offshore smoke troops did provide screens at Port en Bessin where both British and Americans were bringing ashore fuel oil and lubricants. Here, in coordination with the British, the smoke trawlers stood ready to provide screens at twilight and during nocturnal red alerts as long as this important facility seemed threatened."
"During the critical period while the Allies were fighting to secure a firm foothold in Normandy, the landing beaches were virtually free from bombing from the air, and the need for beachhead and port screening did not materialize."
TL;DR - No enemy planes, no need for smoke.
Source