Short answer: yes.
Long answer: yes…but it doesn’t have to be as formal as you may think.
Copyediting is absolutely essential for the road to publication. It will correct the majority of errors in spelling, grammar, vocabulary, and sentence structure. The time an editor has to invest in your manuscript will vary—everyone has their own method—but typically you can expect an editor will give your document a minimum of two passes before the deadline, rendering your work of art near perfect.
Following copyedits, then your review and application of them, you should have a proofreader scheduled to give the manuscript a final once-over. The last polish, if you will. This is a task of equal importance to the copyedit, because the proofreader is the last man standing. The switch-flipper who says, upon completion, this book is ready for the masses. As a pair of fresh eyes, they will catch any minor errors that may have slipped past your copyeditor, bringing your novel to peak performance.
Budgets are tight, particularly for self-published authors, so it is understandable that you may want to opt-out of hiring the services of both a copyeditor and a proofreader. But that final review is critical.
Do you have a friend who excels in English and hasn’t yet read your book? Offer them a free copy in exchange for their time and a red pen! A lot of authors have groups of beta and alpha readers who give feedback on their novels—ask them to note a mistake should they catch one.
While I’ll always promote having a professional complete a task, it’s better to have this done than not. Your book will shine, and you’ll have more confidence as an author when publishing.
In the majority of my copyediting work (I’m slowly but surely switching to this across the board), I make initial edits, send them off to the author, and revise once more following their review. This additional revision isn’t intended to replace proofreading—fresh eyes, fresh eyes!—but being as thorough as possible, when time allows, only benefits the novel and its readers.
So, in conclusion: get your book copyedited. Then get your book proofread. And the more people in your circle that can read it prior to The Big Day, the better.