Indeed, in the United States vs Reynolds Supreme Court case that seems to be considered the seminal [1] to establish the State's Secret Privilege:
The district court rejected the formal claim and ordered the documents
be produced; but, the government refused and the court entered final
judgment for plaintiffs on the grounds that the refusal to produce the
documents established the Air Force’s negligence.
It seems the same logic could potentially apply here?
Sadly I don't think so. I believe in that case it was certain that documents did exist and one party was just refusing to produce them. In this case, the NSA is neither prosecution nor defense, and therefore doesn't have the same disclosure requirements. Further, there's no proof the NSA has such records. But, like most people in this thread, I am not a lawyer.
[1] http://law.lclark.edu/live/files/9577-lcb111lyonspdf