Actualy, It\'s a couple of questions:
With the the (new?) developer console it is possible add domains to apps for free without using Google Apps. But you will not be able to use HTTPS without registering the domain with Google Apps.
So the answer to the first question is "Yes" (presuming TLS is not required). The second question is not relevant. And as for the third question, multiple domains can be linked with the same application (without using Google Apps).
I can't currently find Google-blessed documentation to support this. But I am currently serving an App Engine application on a domain that is not registered with Google Apps.