I certainly wouldn't doubt there were isolated incidents of shotgun use by airborne troops. However, I just went over the Mark Bando's definitive site on the 101st and did quick search. No information about shotguns there at all. Furthermore, it is generally believed they weren't used much at all in the ETO.
My research books on the Airborne in Europe don't make any mention of the trench gun or any shotgun.
Keep in mind that Airborne troopers were scroungers by nature since they would jump in with precious little gear. So, its not outside the realm of possibility, but it was not issued to airborne units. And remember that CQB was not the standard means of engagement in Europe compared to the Pacific where the 1897 was widely used by the Marines.
Might want to do a little Google-based research and see what you can find out. I'll see what I can uncover.