No.

Large scale airborne operations of the sort you are talking too are a waste of men and resources. During WW2, the airborne units were incresingly used as very tough infantry units because only the best men were allowed into them, and this was their most effective role. This led to them being used in all the toughest battles, which made them even more effective as they were battle-hardened, but it also led to a high level of combat fatigue (which is why the 101st airborne was in the Ardennes in 1944, they were their to rest in an area with a supposedly low risk of battle).

The success of the German Army after Crete shows that airborne operations aren't necessary for offensive operations, and so it is perfectly feasible for operations such as D-day to have gone ahead without them. The D-Day airborne assualt had one or two successes, such as the capture of the Pegasus bridge, but overall they were generally chaotic and ineffective and served no strategic purpose.