Yes and no. Tests that are not written well can be a burden. After code changes, a lot of time can be spent fixing test "failures" that are more a failure of the testing methodology than the app under test. So test, yes...automate, yes...but EDIT those tests and AUDIT those tests, to make sure they are all really useful.
Absolutely, a poorly written/unmaintainable/or inaccurate test can have a negative net worth.