Strictly speaking, no.
Spelling and grammatical errors are not ranking signals. Google doesn’t care about your typos. (Proof? Lorem Ipsum text can rank.)
However, SEO editing (that is, making strategic, data-driven decisions to improve how well your page ranks for the keywords you’re targeting) absolutely can improve your search engine rankings.
And, as a professional editor, I know that SEO editing (just like any other kind of editing) can easily introduce new errors into the text.
So, proofreading isn’t important for SEO, but proofreading is an essential step in any SEO editing process. Why? Because you’re not just writing for robots. Search engines bring you the readers, and it’s your job to maintain your reader’s attention.
Nothing ruins the reading experience more quickly than sloppy copy.
What is Proofreading? Is It the Same Thing as Editing?
In the publishing industry, editing and proofreading are totally different processes. In fact, many editors don’t proofread, and many proofreaders don’t edit.
After an author has drafted and self-edited a text, it’s sent to an editor, who helps the author improve the quality (clarity, conciseness, and flow) of the writing. The role of the editor is to work with the author in the service of readers.
Proofreading takes place later, after the layout phase, on the “page proofs.” Proofreading isn’t editing or revising. Proofreading is simply the practice of ensuring the final, published document is as error-free as humanly possible.
SEO optimization without proofreading—or any kind of optimization which introduces grammatical or mechanical errors—is a classic case of one step forward, two steps back.
In my view, SEO needs to improve the quality of the writing, not detract from it. Because frankly, compared the humans reading your content, Google can be fooled rather easily.
TLDR
Proofreading doesn’t matter for SEO. But do it anyways.
P.S. Need instructions? I’ve written up my start-to-finish process for proofreading a website, including all the tools I use to make website proofreading as painless as possible.