Sometimes yes, but generally no.
The author of a work has a copyright to the work as soon as it is created. All s/he has to do is “fix the original work in a tangible medium of expression,” meaning either putting pen to paper or just saving a word document.
An author can either retain their copyright, or assign it to a publishing company. If they assign the copyright, then the publishing company now is the owner of the copyright. The advantage of assigning the copyright is to have someone more experienced fund and manage your book career; the benefit of retaining the copyright yourself means that you can decide how your work is creatively expressed, such as if it’s adapted into a movie.
Next, the copyright owner has a decision whether or not they want to formally copyright the work with the Copyright Office. You can register literary works with the form TX. The copyright owner can publish the book at a much later date. Publication isn’t required for a work to be eligible for copyright protection.
For example, the copyright date that you see on the inside of the book jacket likely coincides with the date of formal registration or the date that the work was finished and submitted to the publisher, but not the time that the book was first written, which is when the book first earned its copyright.
If you have more questions about copyrighting or publishing books, feel free to contact New Media Rights at (619) 591-8870 or firstname.lastname@example.org for free, pro bono legal assistance.