WordPress, and many of its plugins, store configuration data in the database. That alone could cause issues for the setup you described, but the urls of every link will also be stored fully canonicalized. So, unless you plan to test your staging setup from “http://localhost“, you will have serious issues trying to click around multiple resources for testing.
It is far better to setup separate databases, and not just because of the difficulties I have outlined. Having completely separate environments frequently exposes flaws in programmers’ assumptions. The more often you distribute and re-test software, the more flaws appear before they reach your production environment.
If you want the same exact content in both places, I recommend you write an automation script or two, to perform the migration as quickly as possible.
In any case, I would very strongly recommend against pursuing the environment you described.