No, it would have no legal effect whatsoever: something that a person says or writes unilerally (on their own)  does not create a binding or enforceable agreement or promise. To make this enforceable, not only 1) would the employer have to demonstrate that it agreed to it, such as by countersigning the letter, but also 2) you would have to give the employer something of value (the legal term is "consideration") to bind the agreement, such as by agreeing to not receive some pay or other compensation (if any) to which you are otherwise entitled, providing some free work or consulting for the employer, etc.