No, there is not much room for adjustment, maybe a millimeter or a bit more. I think this is only for "fine tuning", the rough height adjustment has to be done beforehand using a file.
I doubt there would be room for adjustment for significantly different bullets or loads.
My feeling is the following: this sight looks quite "old-fashioned" for your rifle - it looks right for a muzzleloader, but your rifle was made sometimes between the 1890s and 1920s (BTW, you will be able to date it from the number of the Ferlach proof house which should be there). Maybe the owner of the rifle specified this rear sight type because be was used to it and did not care about switching loads.
fuhrmann