Uncensored2008
Libertarian Radical
No it would not. If you are administratively discharged from basic training it's as if you never joined at all.
I joined the Army in 1983 based on some tests I took. The recruitment was into OCS. After 4 weeks, we were gathered into a room where the Sargent informed us that there were too many applicants, and that half of us would be dropped into general infantry, OR we could opt out.
No one knew what half was what, and I wasn't going to take a chance, I opted out - as far as any records are concerned, I was never in the Army. As you say, it's as if I never joined at all.