Is it possible to access a webservice through an Android app? So basically a user would be purchasing access to the site by paying for the app? Then deploy rich content to the user through the browser? If so, is it then possible to authenticate who has access to the site from the webserver without the need for signin or signup?
Yes that all sounds possible. Do you have a specific question? Is sure wouldn't pay for an android app that was just a browser to your website. But that's a personal thing.
Is it possible to access a webservice through an Android app?
Yes, and many many apps do so. Not all web-services are equally friendly for App development though. Does the webservice in question have an API designed (read: usable) for this?
So basically a user would be purchasing access to the site by paying for the app?
Yes, if its your web-service, or a web-service that allows this type of licensing/usage.
Note: I, as a user, dislike Apps that are only facades for mobile websites/web-services- Id rather visit a mobile page/service in my phone's web browser.
Then deploy rich content to the user through the browser?
Yes, depends on the content though, this isn't the only way for an App to interact with a web-service. See my note above.
If so, is it then possible to authenticate who has access to the site from the webserver without the need for signin or signup?
Yes, I am not sure if there are existing solutions for this, but it would definitely be possible to roll your own.