So here's the thing. I love my social media pages - only facebook at this point. I have 124 friends on it. Those include more than 6 decades worth of friends. Yes, there are a few that I met on the web. As a writer on many content sites, one forms relationships with others, and they become friends.
I don't, however, ever use my social network to promote my writing. I don't bother to promote my writing. All those 5 star reviews I got happened organically over a period of time - a long time.
Am I successful?
Not if you are going by money. And not if you're going by fame. I remain a nobody.
But I can pay my rent, and pay for food, and I love doing what I do. I don't have to pretend to someone I'm not, and I don't have to please people for the sake of a book sale or a read.
So, it really depends on what you want from your writing. Do you want fame and glory and immense reach? Well, then that's a bit harder, I suspect.
If you just want to be free to say what you need to say, to let it fall where it falls, and to earn some money to pay the rent, then, yes, it's possible to do it without social networking.