Is it worth to check "too green" automated tests

Its been quite a while since my last post... Let's try to reactivate this blog!

Just stepped into a test blog recently, Test Project. They have quite some interesting articles there including one about how to test tests. It is a little superficial, but just made me thought about "green tests". If there is a test that since years is being run on the build server, and never failed, is it a smell? Is it a useful test?
First I  would say it depends on how the automated testing infrastructure is setup. Let's say the developers must always run a suite of tests on their end (and they actually follow the process, or the tolls make them), then you cannot say that the test is "too green" in the build server, as the possible false assertion never reaches it. But if there is a Gated check in, or tests that are only run on the build server side, then it would be interesting to make some measurements to check when this tests last failed. I will give it a thought :)