This situation happened to me many years ago, in the late 60's.
I graduated from HS in '65, at the age of 17 (yes, I started first grade when I was four).
There was no way that I would attend college, regardless of my desire (it's a "family thing", which I won't discuss on a public board).
Anyway, since I was only 17 but had a strong desire to acquire additional education, I did apply and was accepted at a local technical school that was being developed in an effort to start the first community college in our area. At the time, these schools (community/junior College) were not available in our area, as they were in the West Coast.
I took the test and was accepted into their "Data Processing" (not IT, during those years, since a lot of work was being done on unit record equipment - not computers). The course was one year, covering the course material they expected to cover in two years, once the community college was set up. They were able to do this by concentrating on the core subjects, while leaving the "filler courses" out of the program.
I was expected to finish (and receive a certificate) in June, 1966 at the age of 18. However, I was well aware of the buildup of troops for Nam and the draft was alive and well - with no lottery system at the time. Assuming you turned 18 (and was found physically fit), you were going to be drafted, unless you had some type of deferrment - which I did not.
Since the technical school was not "accredited", it would not qualify me for a deferment, as college would. However, I had a strong desire to finish up but faced the fact that in January of 1966, I would received my notification to report for my pre-induction physical, followed shortly thereafter by my induction (draft) letter.
To avoid that situation, I enlisted in the Air Force, under their (at the time) "delayed enlistment program" in the fall of 1965 when I was still age 17, in which you were committed to the AF, but did not have to immediately report for service. This would allow me to finish up my program and select a date for my induction (which was planned for two weeks after I graduated, in June 1966).
As the time came closer, I received a letter from the AF saying that my induction would be delayed three months (till September 1966). While I was a bit upset, since I had already made plans for my leaving (and I needed to leave home, but had no money to do so), I figured I would work around the problem. Unfortunately, due to the continued buildup in forces for Nam, and the backlog in training for AF personnel, I actually started basic training in February, 1967 - eight months after I originally planned for. It caused a lot of personal problems (since I was expecting on leaving home to avoid that "environment"), and added 8 months of "hell" to my existance, at the time.
Just to comment on the possibility of delay (although for different reasons). It happens...
PS: I did receive my pre-induction letter from the draft board (there was no link between agencies at the time - they had no idea that I had already signed the papers to enter the AF) in January, two weeks after I turned 18. The writing was on the wall - for a lot of folks in those days.