Otherwise, look to the history of your company. How have your boss and other managers handled employees' resignations? If you see a pattern of upper management refusing to let the team members work out their notice, you can likely expect the same.
Sure, it may sit in the depths of HR until the end of time, but you can be sure of two things: One, your former boss (and future reference) will read it and be impressed. And two, if you ever decide to come back to your company (hey, it happens), it's a very good thing that last thing on file is a great, professionally written resignation letter.