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.
Why a Resignation Letter? In these digital times, why should we submit a resignation letter, anyway? A paper trail does seem old_fashioned, but in this case, it's a best practice. It makes your intentions clear, as well as the conditions. You're removing any ambiguity about the end of your time there.