MoreUnit is a tool to assist in unit testing. If your tests are doing anything with a database, they are not unit tests. The reason for this is that if you test your class with a real database connection, you are also testing the database along with your class.
You should decouple your dependency on the database with a mock (see my answer here for an idea how to do this).
If you are doing data-driven tests, then it would be better to use a tool such as DbUnit to drive your tests rather than relying on a real database connection. With such a tool, you will have control over the data for each test and won't have to worry that tests fail because someone else updated data in the database or that you executed your tests in "the wrong order".