Does one usually get a notification of receipt of a PhD application?
It really depends on the school, and the channel of communication. I usually follow up after a week of sending an email if I were applying to a specific professor.

Using the example of my school, PhD applications are handled centrally, and you only get an email of further inquiry or rejection.

In either case, there are probably a lot of applications that the professor needs to sort through, a smart follow up is usually necessary.