No, The holster is American commercial not German military. It appears to be an Audley..not a model I am familiar with. An Audley will usually have a spring loaded trigger guard knuckle that holds the pistol in the holster. I can't see if this holster has it..
If it does, it will rub the trigger guard damaging the metal and finish. I don't like Audleys for this reason. metal on metal.
This pistol would have been mated with a full flap hardshell Imperial German Luger military holster dated the same as the pistol.
Here is a link to a WW1 holster of the type.
https://www.ebay.com/itm/German-Impe...IAAOSwbK5foAAg
This eBay holster is dead as the magazine pouch is destroyed. But this type was used almost from the inception of the German Luger into the German Army until WW1 ended. at this time the style of the German Luger holster began to morph into some different variations and in around 1926 changed in important ways into the WW2 type.