It was; like all the pieces of the Overlord puzzle, tantamout to success. The disruption in the rear areas severely hampered German reactions to the invasion. Many objectives were never truly completed, but the ultimate and base objective of establishing a (relatively) cohesive force in the immediate rear - what's called a 'vertical envelopment' was established, despite great confusion and the strategic blunder of a mass airborne operation at night.
I'll settle with two examples;
In a form of compromise between Rundstedt and Rommel, a single armored division (21.Panzer) was kept within 'immediate' striking distance of the British beach-heads. The 21.Panzer's route-of-approach took it past Ranville, over the Orne canal. The unit was decimated in combat by elements of the British paras and glider infantry (towing much needed AT guns!) who had set up a blocking position there during the night, and forced to withdraw for the day. The Ranville defense would come into contact with forces pushing in-land that same day. In short, the blocking position set up there ensured that the arriving invasion force had a vehicle-capable bridge to cross, and that same bridge would be denied to the enemy.
In the US sector, Paras were dropped nearest the Utah beach causeways. Their subsequent actions have been the subject of endless forms of media of varying accuracy but the bottom line remains: units that should've been moving to secure causeways were instead sending precious detachments of men to contain, find or destroy pockets of Paratroopers. Further, immobile artillery units were either over-ran or pinned down by harassing attacks in the areas of St. Marie-du-Mont, St. Mere-Eglise and Fauville. The proof of their effect is in the numbers; if memory serves me correctly, Utah beach suffered just over 200 casualties and took only a light amount of defensive artillery fire. The holding of key towns near the 'mouths' of the causeways allowed for early link ups between the 4th ID, the 505th PIR (much scattered though they were) and separate tank battalions.
It should be noted that several key objectives were never actually seized; such as the Merville Battery (only 2 guns were in fact put out of action) but do not discount the fact that an artillery group defending itself at close quarters over the span of several days only has a minimal ability to do its actual job. In cases where assaults were repelled successfully, batteries would then have to be protected against further efforts; requiring riflemen - further siphoning manpower off on 'secondary' tasks. This goes beyond a nuisance effect, and can be equated to a pinning attack, forcing an enemy to commit his reserves prematurely and thus leave his line easy to crumble.