Short answer: No. According to my research, the German-marked guns were nearly all in .32 ACP caliber only; just a few in .380 ACP only. I believe that the gun you referenced with two barrels and two mags was probably put together outside the factory.
John
There are 3,200 recorded 10/22s in .380 ACP. It is inaccurate that the 10/22 was issued to West German troops, the 10/22 was instead issued to the police.