Okay. Not completely impossible.
Early 15th century, the head of the house would be Amadeus VIII, who was elevated from Count of Savoy to Duke of Savoy. (Knowing the history of the titles 'Count' and 'Duke' makes this somewhat ironic, but that's really a sidetrack.) Amadeus was a powerful man in the Empire, a favorite of Emperor Sigismund, AND the last historical antipope, Felix V. (And yes, if you're wondering, he was married and had kids before he became "Pope". Look it was a funky time for the Papacy, okay?) So it's not completely inconcievable that he wind up HRE. Just... unlikely.
That said, you'd probably be better served going back a few generations, and having them get some German land...