Of course, but it is fairly obvious that it is basically the versions from the book that D&D borrowed, not the "authentic folklore" versions.
My point being that it's mostly the fantastic elements that influenced D&D, not the historical elements. That makes sense, because the focus of the book is also on the fantastic elements, not the historic ones. The Law/Chaos elements of the alignment system seem to have been particularly influenced by the book, as well as the paladin class.
Edit: Three Hearts and Three Lions may also be the first book with a Scottish dwarf. That certainly had far-reaching consequences.
Also, I would say Thyatis is more of a Roman Empire/Byzantine Empire expy than a Holy Roman Empire expy, as is made clear from the artwork, the gladiatorial arenas, and names used (Latin and Greek-derived, not Germanic). For instance the Thyatian-colonized Grand Duchy of Karameikos (Greek) has Specularum (Latin) as its capital.