My general answer.
I would pipe in with the general consensus: usually, paying for an essay that you never use is not cheating. I feel like people who are saying "well, you funded the cheating industry" have a somewhat valid point: you probably don't have warrant to feel proud about what you did and might even feel bad about it. But the question of "cheating" is, "did this give you an unfair advantage over the other students," and in the usual case, that is "no."
However, please note that a university policy on cheating may forbid things which are not themselves cheating! The classic example is if, after you've taken a course, you write an essay for someone who is currently taking it: you might be kicked out for helping someone cheat even though you didn't cheat yourself. Your university's policy may also ban paying for essays even if you don't use them as a matter of course. So if we're not talking about "cheating" but "violating the policy on cheating" then we need to know the policy.
Now let's get clever.
To me this is actually a fun question insofar as we ask, "well, what about that word usually up there: you said it's not usually cheating, but how unusual can we make this?" In other words: are there situations where you can pay for an essay that you will never read or submit, and you still somehow use it to cheat? And the answer is yes.
As a vehicle to explore this, I would like to introduce you to Dr. Alicia Alice, who teaches at the University of Cheating (named for the city it is in, of course). Her course is in Advanced Floozels -- do not worry about this word, it is a nonsense word. Unbeknownst to her, lots of her students are rather amenable to cheating in principle.
Dr. Alice has a very strange policy for her Advanced Floozels course: since nobody can truly memorize everything there is to know about floozels, her final exam begins with one essay question: students must, in a 24 hour time period, research the given question and write an essay response. She wants to give them some ability to study for the exam by guiding their general research on floozels, so one week prior to revealing the question, she reveals 10 possible essay questions, one of which is going to be the chosen question. Let's also say that there are 30 students, with the top 10 getting a significant boost on their actual final exam and the bottom 10 getting a significant penalty.
Bob and the random testing insurance
Bob only finds a small niche of floozel knowledge interesting. When the study week begins, he only really likes one of the questions, so he buys the 9 remaining essays from people who have taken Advanced Floozels before, for each of the other questions, and then he spends a week studying only the one question that interests him. Bob is very lucky: Dr. Alice chooses this question for the exam, he writes a perfect essay with eight whole days' research behind it, and he rockets into the top bracket.
Bob has gained an unfair advantage over the other students even though he did not read or submit the 9 papers he paid for.
Carol's curvy screw-up
Carol and Dennis are also taking Advanced Floozels and Dennis wants to spend the test day goofing off, even though he is a great student. He offers in advance to pay Carol, another good student, for her essay, so that he can rewrite it in his own words and try to pass off his essay as independent work. Initially, Carol accepts his money and agrees. However, when the essay question is revealed, she chickens out and wants to return the money. Unfortunately, Dennis is out whitewater rafting and she is unable to reach him by phone or text to retroactively decline the offer. She therefore instead approaches her friend Ellie, who now does some floozel research. It turns out that the question is very similar to Ellie's research from last year and so Ellie offers to write (for some of Dennis's money) a paper which looks to Dennis like it is cutting-edge research but which Dr. Alice will realize is total garbage. Carol agrees.
This is not always cheating, but we could maybe expect that Dennis would get a slightly better paper in than Carol's, so if Carol was just between two of these categories (bottom 10 gets penalized, middle 10 is neutral, top 10 is rewarded), tanking Dennis might give her a reward that she wouldn't have otherwise had, had she not agreed to this whole strange state-of-affairs.
Anonymous exams which the instructor nevertheless reads.
There are a lot of ways to cheat if we broaden the "I didn't submit it" to "I didn't submit it in my own name." For example, we can do "insurance" this way too: Felipe might pay for and submit a nameless exam and then intentionally not write his own name on his exam. He does this because he's taking a very difficult risk on his own paper, writing about some very cutting-edge floozel research that will either be extremely forward-thinking to Alice, or else will seem like complete drivel. Now when she has a paper with no name, the compassionate Dr. Alice grades both normally and posts both publicly, and expects them to get back to her. Felipe looks at the nameless posts and sees that his paper, in fact, has the highest grade there, so he claims it as his own and apologizes for not writing his name on his essay; perhaps she even asks him to prove it and he shows her the original file on his laptop.
Other people claim their papers and Dr. Alice has no idea who the 31st paper belongs to, and cannot necessarily prove that anybody was cheating. Nevertheless, we know that Felipe was: similar to Bob, he was buying a "safety net" which other students did not have access to.
Or, Gertrude might buy so many low-quality papers and submit them anonymously that Dr. Alice realizes that something has gone awfully wrong, and might ask everyone to privately email her their submissions from their school email account instead, since that will be better-tied to their identity. Gertrude uses the extra time from this distraction to gain an unfair advantage over other people who have completed their essay on-time.
Harold pays for an anonymous essay which ultimately insinuates that if Dr. Alice failed any of her male students, she would be subjected to physical danger. The police are unable to trace it and she is scared enough that she doesn't fail any of them, and then Harold has an unfair advantage over the female students. (Technically this doesn't have to be submitted, but it happens to be the best way to ensure Dr. Alice or one of her TAs reads the work.)
Irene pays for an essay in the sense that she pays someone else to steal some early drafts of several essays from some of the top people in the class, with the explicit essay being composed of complete sentences from all of them weaved into a cohesive narrative. She does not read them directly but anonymously posts it to FloozelTalk, the premier floozel research chat forum, where Dr. Alice reads it and thinks it's cutting edge research being done as we speak. Dr. Alice penalizes everyone who appears to have plagiarized this essay, and Irene thereby gets some benefit from it.
Then there are the ones which go outside the box completely.
Implicit in this I have been looking for solutions which use the information content of the paper but, I mean, it's also a physical artifact as well. Jacob pays for an essay which is 300 pages long (needing it to be a coherent essay just in case someone stops him and demands to see it, for example) -- and then he rigs it above the turn-in slot so that he drops it on Dr. Alice's head as she is picking up the papers, knocking her out cold: he then anonymously calls an ambulance and uses the added time that she is recovering in the hospital to complete his actual essay.