It is really risky. I really respect your efforts and success on quitting alcohol and adjusting your life back to a normal track. I think that it is GREAT, and congratulation. I really mean it.
However, adding on the existing accepted answer, I believe that you are misunderstanding the application essay as a whole. The essay "what are struggles have you overcome", is NOT about "Struggle", it is NOT about "Overcome". It is about using this essay to show you are hardworking, talented, positive, passionate, kind and earnest.
This applies to every other essay, regardless of the title. I would like to point this out because from my past experience and my communications with my fellows and friends, for some reasons, cultural, personal, etc, we focus on the title too much. Of course, you can't just write completely something else or just saying you are good. You should use struggle and overcome as a stepping stone to start a good story talking about good things about yourself.
In your essay, you should just describe that "struggle" for 2-3 sentences. You should not even talk about a "real struggle". What I mean is the following:
A real struggle: I was an alcoholist and my life was in the wrong path for a really long while.
A "good" stuggle: My family was not economically sufficient, so I worked part time in a public library to 1) earn some extra money; 2) I can secretly read my beloved mathematical books, and copy down what I saw important in my note book. When I finished working back home, I would review them and bring them to my dream. (Yeah this is bad wrtting, but you get what I mean).
Write something positive, really passionate, really motivating. Show them you are a positive person, filled with passion and motivation, DESPITE your struggle.
Your struggle serves as a tool to show you are GOOD. Your struggle is not just a struggle. It is a special experience, a valuable period of time, in your life, that made you a better person. And, you appreciate this struggle you had.
In the application essay, everything bad should be written in a way that even the worst thing is the best thing. You should write them in a firm and positive way. You should show that, you trust your ability, you believe that you are a good person and you are talented, from the first day since you were born.
I understand that this sounds really "fake" and hypocritical. And it seems like the whole application essay is just a facade. This is what it is. And your goal is to get in the school you want. With some tweaks, you will write the essay in an honest, yet good way. I am not saying anything about faking your essay. But, everything has two sides. You should write the bright side only.