The short answer:
Sometimes it can count for a lot, and sometimes it doesn’t count at all.
The long answer:
While Writing does not count as much Critical Reading, it still does count at most schools, so it’s advisable to take the section seriously. If a school does not consider the score, there will be an explicit announcement on the admissions page.
If you’re scoring in the 700’s on CR and in 500’s on Writing, which is unlikely but theoretically possible, you can’t assume that admissions officers will be willing overlook the lower score because “it’s just not that important.” Everything is important if you’re trying to decide between five — or ten — similar applicants.
They probably won’t take the time to read your essay, or even care about the essay score unless it’s exceptionally low by their school’s standards, but the overall score will definitely count for something, however small. Most likely, it will simply serve to confirm the impression they’ve gotten from the rest of your application.
At the most selective schools, a good score (750+) won’t necessarily help you, but a bad score can definitely hurt you. It’s considered a given that you’ll score above 700 at absolute minimum; if English is your first language, anything below that is a warning sign. And at some less selective schools, a good writing score can actually help quite a bit. The majority of colleges — even test-optional ones — love to brag about their scores, and so if you’re not applying to Harvard and just can’t stomach trying to pull your Critical Reading score up, you can still help yourself by focusing on Writing.
The good news is that Writing is comparatively easy to prep for; the bad news is that you still have to put in the time.