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.
Even if you're not close with your boss, chances are you have a working, first_name_basis relationship. Maintaining that in your official letter is okay. You don't need to keep a Victorian level of formality here__just make sure it's a professional tone.