Some people in the translation business certainly seem to think so (although I personally could not vouch for them, I just found this on the internet).
First, there might not even a mystery to explain or mistranslation to deal with. The Balrog is not addressed with "Sie", because in the books and the movies nobody is. That would simply not be German appropriate to the setting. If anything, it should either be "Ihr" (if Gandalf feels that he own a fellow Maiar at least some respect) or more likely "Er" (but even "Erzen", which is actually a word, might be too modern). However I have not read the Krege translation, which might be relevant (since it is "modernized" and might have used modern forms of addressing people).
(As pointed out in the comments, Krege actually did use the formal "Sie" and other modernisation to get closer to Tolkiens original pretense that LotR is a translation from an ancient language. I disagree with that for a number of reasons, but obviously the Krege's professional judgement carries much more weight than my personal taste).
The sentence as spoken is just as appropriate to the setting. As the Germans say, it lacks the necessary "Schöpfungshöhe" (originality, basically) to make it identifiable as the creation of a specific author.
However the German dialogue was written by Andreas Fröhlich, who also more or less by accident became the German voice of Gollum (as he tells it, they forgot to book a voice actor for Gollum and he took over the role so successfully that he repeated it for parts two and three).
A search for "Fröhlich/Carreaux" did not find any immediate connection (they both know/knew German critic Denis Scheck (not at the same time, as Carreaux died in 1991), but that seems to be the level of their personal connection), but led me to a message board frequented by people "in the industry".
One of the users there writes:
Ein weiteres Beispiel in dem die Frage einer freien oder
literaturgebundenen Übersetzung für die deutsche Synchronisation zur
Debatte stand, ist zwar kein Klassiker ansich, aber auch
erwähnenswert: Peter Jacksons Der-Herr-der-Ringe-Trilogie. Die
Drehbuchschreiber verwandten eine Vielzahl von buchinternen Zitaten
bei der filmischen Umsetzung, änderte manche minimal, oder setzten sie
an eine andere Stelle im Handlungsverlauf.
Problematisch war hierbei vor allem, dass die Verantwortlichen der
deutschen Fassung zunächst eine Entscheidung zu treffen hatten, welche
Übersetzung der Bücher als Basis der Synchronfassung, so notwendig,
dienen sollte. Im Jahr 2000, also noch vor dem Erscheinen des ersten
Filmes (Die Gefährten) war eine neue Übersetzung der Bücher
erschienen. Wolfgang Krege (1939–2005) versuchte durch
Modernisierungen und sprachliche Belebung einen neuen Zugang zu dem
Buchstoff zu schaffen. Inwiefern ihm das gelungen ist, muss jeder
selbst entscheiden. Der Verlag nahm daraufhin die erste Übersetzung
Margaret Carrouxs (1912–1991) und Ebba-Margareta von Freymanns
(1907–1995) vom Markt. Da es aber diese Übersetzung war, die ein
Großteil der Fans eher zusagte, stand der zuständige Verleih der
Trilogie (Warner) vor einem Problem.
Man entschied jedoch zugunsten der alten Fans und damit für Carroux
(womit man Krege jedoch nicht komplett fallen ließ). Als Berater soll
damals Stefan Servos fungiert haben. Da er einiges veröffentlicht hat,
und Forumsleiter von herr-der-ringe-film.de ist, nehme ich an, dass er
maßgeblich an der Entscheidung beteiligt war. Andreas Fröhlich
arbeitete als Dialogbuchautor sehr genau. Er schaffte es zum Beispiel
bei Passagen, die inhaltlich aus Eigenformulierungen und Buchzitaten
zusammengesetzt waren, das entsprechende Zitat in den Büchern zu
finden und, soweit möglich, wortwörtlich zu übernehmen. Dabei
entschied er auch, ob er Carrouxs Übersetzung wörtlich übernahm, diese
abwandelte, oder sogar manchmal Formulierungen Kreges einflocht. Dabei schien nicht nur die Lippensynchronität entscheidend gewesen zu sein, sondern auch die Atmosphäre der Szene.
I will translate a bit more later when I have time, but the bolded parts say that the movies use a lot of quotes from the books, that the people in charge needed to decide which translation to use and that to appeal to long standing Tolkien fans they would use the "traditional" translation (i.e. Carroux, the Krege translation being new and more "modern"). However some elements of Krege were included.
The last bolded bit seems especially relevant. It says, in a very rough translation:
Andreas Fröhlich is very precise when he creates dialogue for a movie.
For example, in passages that are partly original creation and partly
quotes from the books, he manages to locate the corresponding quote in
the book and, if at all possible, use it verbatim. This includes a
decision between using the exact phrase from Carroux's translation,
modify it somewhat, or even uses phrases from the Krege translation.
Nikolaos Aslanidis wrote the thesis for his magister artium on "The difficulty of translating J.R.R. Tolkien’s Lord of the Rings into German". As part of the thesis, he compared text text from the book and the dialogue in the move. Regarding the passage under discussion here he writes:
Chapter 2/9 concludes the voyage through the mines of Moria with
Gandalf fighting the Balrog. Most of Gandalf’s lines here are taken
from the original text.
T 433‘I am a servant of the Secret Fire, wielder of the flame of Anor.
You cannot pass. The dark fire will not avail you, flame of Udûn. Go
back to the Shadow! You cannot pass.’
J 2/9GandalfI am a servant of the Secret Fire, wielder of the flame of
Anor. The dark fire will not avail you, flame of Udûn! Go back to the
Shadow. You shall not pass!
Note that Peter Jackson tries to have Gandalf sound even a little more
old fashioned and possibly even more mystical by changing Tolkien’s
plain ‘You cannot pass’ into ‘You shall not pass’.
(Source. "T" and "J" in front of the quotes refers to Tolkien (ie. the book) and Jackson respectively).
So this is very much a case of book quotes intermixed with Jacksons own interpretations. Fröhlich locating the phrase in the translation that corresponded closest to the phrase used in the movie would certainly fit the workflow outlined above.
So my opinions on originality notwithstanding, it seems perfectly possible that the sentence was taken from Carroux's translation.
