Yes, they can, although the paperwork and process to depart is very time consuming. You don't just say that you want to leave and then depart the next day. I don't really understand why it takes so long when the cadet is choosing to leave, but it does. If a cadet is being disenrolled due to academic issues, honor violations, or other concerns, that process can take MUCH longer if they choose to appeal.
But yes, a cadet who chooses to leave in within the first 2 years or who is forced to leave for any reason in the first 2 years will not owe back time or money. They can also transfer their credits to most universities (at least for the main core classes).