Can applications purchased through the App Store be used after deauthorization? If I deauthorize a computer from the account used to purchase a certain app, will that app continue to work as usual?
The Mac App Store does not currently have the concept of an "authorized" or "deauthorized" computer. If you download an app legitimately from the Mac App Store, it is DRM free (at least with regard to execution), and completely functional on your computer.

The immediate answer to your question is actually that you cannot deauthorize your computer in the Mac App Store :).