I'm going to go ahead and guess "signed off on" was more like "rubber stamped"

Most likely... but the party who was served the order can file for appeal if they are willing to go that route. That said, it doesn't mean any such appeal with favor the party served the gag order.

And the case likely was "we swear it is very important for national security, trust us!" and that was enough. Search request is almost never refused, e.g. FISA court approves over 99% of them. And if the court already deemed the proof strong enough to do the search, surely it's strong enough to put a non-disclosure on it if asked.