Yes it's absolutely possible to test the application with out test cases but only issue is we not able to tell how much of test coverage is done this is called in Adhoc testing.
With the help of Test Scenarios we can do end to end testing but we should make sure that all the functionalities (major and minor) are covered while testing with test scenarios
Test Scenarios are at high level derived from use/cases and other functional points mentioned in the requirements specification.
We can carry out execution with these but not to a detailed level. As a single scenario is normally broken down to multiple test cases.
Hence testing based on just a scenario will just check the basic functionality missing out on the details.
e.g of a scenario: 'Only valid user should be authorized to access application XYZ'
For the above scenario we will just test the login of application with valid user A and invalid user B without going into detailed testing of the logon screen unless and until we don't have all possible combinations of test cases for the scenario.
One can do ad-hoc testing without test case but for executing you need test cases or at least scenarios listed. Execution is process and for executing you need at least one supporting document.
