Real world here- combat parachute drop is very much unlike a civilian skydiver. Airborne troops are fair game while in their parachutes (unlike a pilot escaping a damaged aircraft). For that reason, they are dropped as low as they can be and still have their chutes deploy. When you jump, your firearm is not in your hands, but in your equipment bag. You will have about 3 seconds between canopy making that lovely CRACK! noise and hitting the ground. You are not going to be firing on the way down.
We do issue earplugs to soldiers now. How much they get used in combat.....
BTW, the personae you mentioned, played by Red Buttons in The Longest Day was a real person- John Steele of the 505th PIR. http://en.wikipedia.org/wiki/John_Steele_(paratrooper