For a while now, I've been reading articles, threads, and all of the like about what makes a good writer (or a memorable/good novel). I know that most writing in general has to be cohesive, memorable, engaging, orderly (unless the style of your writing demands you should not), and unique, but it got me thinking. Can the style of writing be horrible, but the plot and characters of your writing makes your novel great? Because I've noticed (and read) some literature that some would consider "terrible", but the "terrible" books I've read has a similar style, which reminded me of my writing. It's giving me a bit of a shake.
Horses for courses. Some books are known as "page-turners" because you simply can't put them down; you feel compelled to race through and don't even notice the style. Others you open at random and read sections completely out of context for the sheer pleasure of words. I would infer that you are nearer the beginning of your writer's journey, if you consider your writing style to be "terrible", now might be a good time to address that... Get involved in the forum, you will learn a lot simply by interacting with other writers. Down the line, do some critiquing (you can also learn a lot by examining other people's work critically), and then maybe post some of your own work for crit to get some pointers from folk on here. Enjoy the trip.
Since the writing is the sole way of getting those other elements across, you can't truly isolate prose from everything else. Keep in mind, however, internet people will try to tell you a book is 'horribly written' when it's really just that it's mediocre compared to industry greats. It's okay to be mediocre as long as you deliver on your marketing promises. That will still sell.
And not only that, but it's necessary to go through being mediocre before you get good. The only way you get there is through a lot of practice, which means writing some bad stories along the way. Keep paying attention, keep learning, and keep improving. You get there little by litte, not all in one big burst. It literally works like dieting or exercise—you have to work hard and not give up, and the improvements happen little by little over a period of time.
I'd say it can be done, just seeing that others have written works that are stylistically terrible but are still loved. There are some genres where it's completely forgiven. Like say, you're reading a story about a child soldier escaping conscription in the Sahel, and this is written by an actual survivor; no one would much care about strange grammar choices. What's most important are the emotions and unique human perspectives in a situation none of us will ever know. You could read cliches and rambling asides and it would all be fine. It's almost as if the lack of skill carries a certain honesty? If that makes sense.
Just look at Isaac Asimov. Great writer in terms of the story - not so great as far as use of language goes.