TWE and then appointment later is definitely possible. DS#1 is a C1C at USAFA and received TWE (same wording -- no appointment, no prep school) in mid-April 2013, only to get a call from USAFA admissions 2 weeks later with offer of appointment. In my USAFA class, there were at least 4 or 5 of my classmates who didn't receive their appointments until the day prior to inprocessing day. That was a long time ago and things were different then since everything was snail-mail, but an appointment can still happen, even after receipt of a TWE.