Does the above phrase–was der Teufel–work in German the same as the English idiom “what the devil!”? Or would it be broken / nonsensical to a native Deutschlander?
Almost - it would be “Was zum Teufel?” (What to the devil).
“Was zur Hölle” works equally well.
Concur - the German idioms use the preposition ‘zu’.
Google hits for phrases meaning essentially the same thing
“Was zur Hölle” - 1.83 million hits
“Was zum Teufel” - 344.000 hits
“Was zum Kuckuck” - 19.500 hits
Danke!
Tangent:
So … former NY Mets infielder Tim Teufel’s surname is literally “Devil”? 
Yes, Der Teufel is The Devil in German.
I’ve always seen “Was zum Teufel!” translated as “What the he-ll”
so I don’t think “what the devil” is actually a correct translation as the OP asks. That is, it doesn’t work the same in German as English.
Yes, it was delicious when Jim Gott pitched to him.
The former prime minister of Baden-Württemberg was also called Erwin Teufel.
I’d say “what the devil” and “what the hell” have the same (non-literal) meaning in English; that is, they’d be used interchangeably. Since Teufel means devil, I’d think what the devil was a slightly better translation. I’d guess “what the hell” is used more often in English though.
And the piece known as “The Skaters’ Waltz” was composed by Waldteufel, which I guess means something like “forest devil”.
They do have the phrase “the devil is in the details” (Der Teufel steckt im Detail) and “who the devil is…” (wer zum Teufel ist…).
-moe
Showing off my horrible German, even though I’ve been trying to learn this frickin’ language for 3 years now.