No historian, but I'd say your interpretation of "united Germany over the individual duchies, electorates, and principalities" is probably sound. Into the middle of the 19th century, there was no such thing as "Deustchland" there was Saxony (several) and Hesse and Prussia, and a raft of dinky baronies etc. The notion of constructing a "Deutschland" to unite all the "germanies" was somewhat radical and needed a good song. The iconic song of the Nazi period was The Horst Wessel Lied.