Short answer: Yes, if you do it right, so that they work.
Long answer: Here’s Chuck Wendig’s much more extensive answer to this same question.
Chuck provides many instances of authors using sentence fragments, or as they’re sometimes called when used on purpose for effect, English minor sentences. But he doesn’t illustrate this with the example that leaped to my mind which is this:
An April night in Atlanta between thunderstorms: dark and warm and wet, sidewalks shiny with rain and slick with torn leaves and fallen azalea blossoms. Nearly midnight. I had been walking for nearly an hour, covering four or five miles. I wasn’t tired. I wasn’t sleepy.
This is the beginning of THE BLUE PLACE by Nicola Griffith, and these few lines sold me on the book. Yes, because of the sentence fragments. I found this opening evocative and I appreciated the craft demonstrated by the use of those fragments. (It was indeed a really good book, btw).
When Dickens introduces Abel Magwitch in GREAT EXPECTATIONS, he suddenly starts using a whole bunch of fragment sentences. I don’t have the book in front of me, so I can’t quote it, but it’s true. Get out your copy and look at that scene.
I’m sure fragment sentences can be used to do all kinds of things, but in both the cases above and also in some of the ones Chuck quotes, fragments are being used to still the action and paint the scene. It’s as though the author is using a cinematic technique, slowing or stilling the camera’s motion to allow the viewer to see the images.
Of course this is not the same as using fragments accidentally because you just can’t tell the difference, which I hope is still rare in published fiction.
Chuck doesn’t mention it, but imo, on the other side of grammatically correct writing, comma splices can be used to give a sense of rushed speech or rushed thought, which can also be useful. For all I know, someone somewhere has even pulled off actual run-on sentences in a way that worked, though I can’t think of an example.
Chuck’s comments boil down at the end of his post to:
Writing involves a series of stylistic choices.
Sometimes these choices mean breaking rules.
It’s okay to make these choices as an author.
It’s okay to not like these choices as a reader.