If your metric is simply "number of terrorists caught" then sure a broken test is better than no test.
But you are ignoring the cost of "catching" innocent people. Plus you are ignoring the cost of the administering the test.
You could dedicate your resources to actual detective work instead of wholesale dragnet operation in the hope that something useful turns up. Makes for good security theater though.
With no tests, the quiet unassuming terrorist would still walk by.
At least with a test with some efficacy at catching legitimate terrorists even with false positives would be better no?
(Going only by the metric of catching terrorists.)