Will Asarum europaeum add a ginger flavor?
Short answer: kinda-sorta, in a weak way.

Long answer: European wild ginger is grown as a ground cover, not for culinary purposes.  It is closely related to American Wild Ginger, though, which can be used to cook with, but it has a weaker flavor than Chinese ginger, less pulp, and you shouldn't actually eat the roots.  I would presume European ginger to be a very similar experience, but only have experience with the American variety.