That would be no.
The division's main job during the campaign was to block approaches by the Germans towards Utah Beach and to also capture and hold causeway exits off the beaches. They were involved in the fighting at Carentan to try to assist in the merging of the two US Beachheads, the other being Omaha, they fought almost continuously for a month before being rotated back to England.
The British airborne were in the British sector during the fighting, no where near where the 82nd was.