"Ethics aside".... What a world we live in! :( But no, it isn't, because it can be gamed like any other rules system. The NSA probably thinks their system hasn't been explored yet, relying as they do primarily on security through obfuscation. One of the greatest pleasures in life is examining "black box" systems and figuring them out. The NSA would be fools to expect that their system is not already being gamed.
The argument works well for privacy advocates because even without regard to revealing classified secrets, the NSA won't be able to demonstrate good efficacy or good value for the money, due to the fact that such a system can only ever "work" rarely. A close look at this ought to also reveal a large fraction of abuse, and waste, in addition to false positives.