Of course not. Most likely, he simply will not always be able to perceive references and quotes from the classics, participate on an equal footing in conversations. But this is not fatal. Feel the need - turn to the classics. There can be no degradation of any kind. There are too many things and areas of knowledge developing intelligence in the world to grieve about the classics.
To fall, you have to be on top. To degrade, you need to be developed. An illiterate person cannot degrade, he has nowhere and nowhere to fall from. Unreadable, not necessarily classics, but desirable, you just stay at a low level of development.
No, it will not "degrade", of course. To "degrade", one must first overcome the stage of degradation; in order to fall, one must climb. No one has died yet from not reading classics at school. But those who read at least something classic did not get any worse. The winner will always be the one who can fend off with the help of mournful Dostoevsky, screw in a couple of quotes from Chekhov, and understand the subtlety of Tolstoy's allusions. Don't worry, don't "degrade".
Of the necessary subjects in school, without which it will be impossible to build a good career - only mathematics until the seventh grade. You can solve linear equations - you have a chance of success in life. Russian will be corrected by an automatic Word proofreader, everything else will be taught to you at the institute and at work.
If you read a little, it will most likely be a bad syllable. If you have a bad style, you will annoy your interlocutors and will not be able to convey your brilliant ideas to the public. If you are a genius in assembling teams, you will be able to find a person who will do it for you.
Intellectuals will look at you like a fool, especially if you do not understand their jokes and try to pass off as "new original ideas" something everyone read in Dead Souls. If you have great charisma, you can make ignorance your thing.
If you read a little, the depth of reflection and emotional life will develop little. People around you will seem like mindless irrational romantics, and then you will have an emotional crisis and you will gorge on the first trash that will allow you to soothe your heartache: crazy trainings for personal growth, drugs or other people's advice. Or an emotional crisis will not happen and you will not understand what the young ladies, parents and friends want so complicated from you all the time, if the world is so simple and understandable, without halftones. If you have excellent empathy or the ability to manipulate, you will live without grieving and you will not notice anything like that.
In general, there is absolutely nothing wrong with not reading books from the school curriculum.
I don’t know how old you are, but, apparently, you are still in school, since the question is so acute :) Well, first of all, if it consoles you, I can say that the school curriculum has been drawn up, of course is not entirely correct. Many works are difficult to perceive at 13, 14, 15 and even 18 - well, there is still no experience of those feelings that the heroes experience, and indeed the system of values and interests is different. The older you get, the more the angle of view changes. So if something doesn't go well at all, then maybe it's just not the time. It is also important that Russian classics - and any other - should be studied in close connection with history, with knowledge of the general context, both the plot itself and the idea of the work are much clearer. Oftentimes, this is where it also fails. Teachers of both subjects play rather big roles. But, nevertheless, on the other hand, in the same school curriculum there is a lot that I would like to thank the compilers for. It can't be that you don't like anything at all. The 19th century does not go - read about the Patriotic War, about the pilot Maresyev, read Gaidar, Rasputin, Solzhenitsyn - as an option. I will not vouch for 100%, but, in my opinion, both in the curriculum, and especially in the lists of literature for the summer, there are always excellent foreign authors who wrote on topics "closer and more intelligible for a teenager" (travel, adventure, navigation) - Jack London, Mark Twain, Jules Verne - anyone! And how many contemporary authors. The problem, I think, is not so much in reading the classics, but rather in not reading in general. It's one thing if, for various reasons, Tolstoy or Griboyedov is not very clear to you. But if you avidly read King, that's not bad. And here's the thing: the more you read good authors, the more you want, there you will come to the classics, and catch up and overtake. If there is a lack of reading at all, or a narrow interest in low-genre literature of terrible quality, then it is bad.