Yes, out of sight may be connected to ausgezeichnet, though whether it is directly connected or a folk etymology isn't clear. [Note: this is a downgrade of my previous confidence due to new evidence and further thought.]
Using the general information from TimR's answer, I did a few searches for "out of sight" and "ausgezeichnet" at the turn of the 20th century to see whether results connecting the two would turn up. I shall divide this answer into two parts: the case suggesting a connection and the room for doubt.
Tying "Out of Sight" to German Ausgezeichnet in English Writing
In the Macon Telegraph, 4 March 1902, p. 4, a very short piece directly ties the German term to the expression "out of sight":
Those who know Prince Henry [likely Prince Henry of Prussia] will say that as a sailor and good fellow he is positively ausgezeichnet, the American adaptation of which ponderous term is "out of sight." (Readex: America's Historical Newspapers; may be paywalled)
The word and claimed etymology also appear in a 1907 novel:
And then we shall be all ass happy ass. It will be ausgezeich-out-out-of-sight-"
[Note] This philological curiosity was given to me by the Rev. Hobart B. Whitney of St. John's Parish, Essex, N.Y. It is a very logical development of English slang from a German word, so familiar to the Second Avenue section of the East Side in New York. -D.B. (Dolores Bacon. In High Places. 1907, p.330. Google Books)
Finally, "out of sight" is attributed to ausgezeichnet by etymological experts from the first half of the 20th century:
Of German origin also are probably such words as [...] out of sight (German ausgezeichnet) (George Harley McKnight. English Words and Their Background. 1923, p.26. Google Books)
German in origin are, most probably, [...] out of sight, a mistranslation of German ausgezeichnet (Eric Partridge, The World of Words. 2015 (orig. 1938). p. 84. Google Books.)
The last one in particular highlights how the translation here can't be literal. Partridge identifies what both the question asker and answerer sisee identify: this would be a mistranslation of ausgezeichnet. If we then go back to Dolores Bacon, it's possible the text is pairing ausgezeich and out of sight as similar-sounding terms or near rhymes: "ausgezeich-out-out-of-sight-"
But Maybe the Connection Is Less Direct Than They Thought
One of the challenges to the previous answer is that the connection to ausgezeichnet is folk etymology, that is, what a few quotes allege about the origin of the word only proves what people guessed, and they do not document where the word comes from. Indeed, that is a firm constraint on being certain of the origin of ausgezeichnet. Maybe "out of sight" already meant excellent before ausgezeichnet was connected to it.
So I want to offer two quotes that highlight the ambiguity of this connection between the two words. The first comes from "A Thousand Miles Afoot in the Tyrol and Switzerland" by Henry Pelouze de Forest, in Travel, Jan. 1896 (Google Books). Pelouze de Forest describes crossing a chasm via riding rails as a long human chain. He describes people fearful, anxious, and glad to have crossed. He then summarizes the experience of the tourists:
The general verdict was "ausgezeichnet," which is the nearest approach to "out of sight" in the language.
This claim is fascinating because the phrasing isn't that "out of sight" comes from ausgezeichnet but almost vice versa: ausgezeichnet approaches "out of sight." In other words, it sounds like Pelouze de Forest offers ausgezeichnet as a German translation of an already-existing sense of out of sight: "excellent" or "impressive." So it's possible that, for this speaker, "out of sight" did not come from German at all.
The only earlier entry that would still suggest a connection to ausgezeichnet is in the June 18, 1891 edition of Forest and Stream, in "The Possum Club Banquet" (Google Books). The following is an excerpt from a description of events:
Mr. Chas Kern was called on for a song and gave one. This was a chef d'œu·vre. It was ausgezeichnet. But Mr. Von Leugerke sang a Platt-deutsch song soon after which was out of sight.
The pairing of three words from three languages suggests some connection: chef d'œu·vre (French for a masterpiece), ausgezeichnet (German for excellent), and out of sight (English for excellent). But it's not clear how firm that connection is. Could out of sight be the Platt-deutsch Anglicization of ausgezeichnet based on sound? Yes. Could this just be three similar words meaning excellent? Also yes.
Hope you don't mind me adding another attestation, this one from from the Shoe and Leather Reporter, August 1894:
The Paragon Needle Co of Boston head [sic] an advertisement with the German word "Ausgezeichnet" the English equivalent of which may be said to be "out of sight". They say: "This refers to our McKay needles. It may be slang, but if you have tried these needles, you will appreciate its full force, for they are "