Yes and no.
An admissions notice is nice validation (I'm given to understand...), but, really, is just the entrance ticket to spending 5+ years striving and swimming in bigger and bigger ponds. The admissions notice isn't validation of intellect or worth.
Personally, I had a crushing round last year: waitlist agony exacerbated by hard personal choices with the direction of my life. Finally, the way out was to ask myself what, exactly, it is that I want out of having a phd (besides the letters, of course) and what kinds of steps I could take towards creating an emotionally acceptable substitute.
Do good, interesting, work and the rest will fall into place... eventually.
I'm happy to give out more details in PM, if you want.