Such a test can be based on a scenario that touches many parts of the system in order to check that no blocking defects arise when using basic functionality. It can easily be performed as intake test before starting actual testing.
Though, such a test is not always suitable for automation. Early in the testing phase for instance, chances on encountering blocking defects are higher, and there's only one showstopper needed to block you from completing the scenario.
View my definition of testing