Your question implies that the determinative factor would be whether the letter contains copyrightable subject matter, namely original expression by the author. From what you say, the answer would be YES. The letter would be protected by copyright as soon as it was saved to disk or printed.
However, you didn't ask who would OWN the copyright for the letter. Perhaps counterintuitively, federal copyright law provides that a work of authorship created by an employee in the course of employment is deemed to have been authored by the employer and is owned by the employer.
I am not aware of any case law on the subject and would welcome further guidance from my learned brethren as to whether there has ever been a court decision on who owns the copyright in a letter of resignation.
Preliminarily, I'd note that the employee was employed until the letter of resignation was delivered and accepted, so it would be reasonable to conclude that the authorship occurred in the course of employment and that the employer owns the copyright. However, it seems fair to say that generation of a letter that is intended to terminate employment could reasonably be deemed to be outside the scope of employment, even if written on "company time." If so, the individual who wrote the letter would be deemed to be the author and hence the copyright owner.
I would add that the copyright owner would need to REGISTER the work of authorship with the U.S. Copyright Office as a condition precedent to enforcing the copyright.
