No, whether that's true depends a lot on the tests and also what you're testing.
I have been in a situation where analyzing results from tests took more time than actually manually finding the bugs *and* fixing them. Eventually we got rid of them. They were quality tests and at wrong level in the stack.
Tests are mostly useful only if:
* they're (mostly) automated
* they produce statistically reliable and non-ambivalent results
* writing, maintaining and analyzing their results save time in the long run
Preferably they should also be mostly auto-generated so that they get automatically updated with the code, there's less code to maintain and issues with it are more apparent.