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No, it's not. To allude to something, or an allusion, is almost like a metaphor. For example, In "Frankenstein" Mary Shelley alludes to the potential dangers of science and technology.
Within the context of literature, an allusion is "a passing reference, without explicit identification, to a literary or historical person, place, or event, or to another literary work or passage."
If you make a passing reference to that quotation, without citing it fully, without identifying the source, that is an allusion. The famous quotation is not itself an allusion, although (with whatever it says) it may allude to something else. For an allusion to work, the audience has to have the background to recognize the passing reference. To take a modern example, the television show _The Simpsons_ is filled with allusions to various persons and events. Part of what makes it work is that we understand these passing references, which are often recontextualized so as to make them funny.
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Allusions mean you use information in your story or work that is meant to make someone think about either: 1)some other important literary work; 2)mythology--can be Classical like Greek or Roman, or other like East Indian, Hopi, etc; 3) other fairly well known data. The writer uses this like "Easter eggs" in online games or software. It works sort of like an "inside joke" for people who can connect the allusion the writer puts in, with the original. These mentions are put in the work to deepen it--giving those that can identify the allusions more insight into the writing, characters, plot, etc.
The key to making allusions work in your writing, is that the allusion is supposed to be relatively widely known information--or at least fairly well known to the audience you want to target. When I was in high school, we were reading Wharton's novella, Ethan Frome. The work was short and the writer was very precise. If she added a detail it was added because it meant something. For example, she mentioned the Pleiades constellation. It was an allusion to a myth where Orion was attracted to 2 of the Pleiades sisters, and was set as a constellation opposite to them in the sky. By mentioning the constellation, Wharton makes a classical allusion. She put it in to foreshadow of what will happen in the plot later in the novella between Ethan and the 2 women in the story.
Naming characters with historical names--think pig in Animal Farm was 'Napoleon'--is an allusion. We are meant to connect what we know about the historical Napoleon, with the writer's character. Sometimes the allusion is meant to point out how the character, or plot follows the original. Sometimes the allusion is meant to point out how different the writer's version and the original are.
Also, to make an allusion work in your writing, you should NOT have to explain it to your audience. If you become famous, that's for people to put in the edited version of your work as footnotes or endnotes! If people miss your allusion, so be it. For it to be "good" writing, the audience should be able to read your work and enjoy it, even if they miss the allusion. For the audience that 'get it', the allusions should deepen their appreciation for the tight way you crafted your story & tied in even the smallest details. That said, allusions--as with all things symbolic in writing--should be treated like salt. Use just enough to bring out the flavour. Use too much and it ruins your dish!