Many American paratroopers were dropped far from their landing areas on the night of June 5/6, 1944, but I don't think any of them went as far East as the Gold, Sword, and Juno beaches!
Of course during Market-Garden that September, American paras held the bridges (at Grave and Nijmegen) for the British XXX Corps. And elements of the 101st AB helped "rescue" the Brits from Arnhem at the end of the operation.
But generally they were pretty separate.