No, it’s not a product of Hollywood’s overactive imagination; there really was a full-auto broomhandle Mauser. Check out the details behind the M712 Schnellfeuer.
Even Colt’s diminutive .380 ACP found its way to war. Here's an example of the Model 1908 General Officer's pistol, used by Brig. Gen. Ridgely Gaither in WWII.