I mean I would not count it out as being one the reasons behind the closings among other theories. One might argue that it is just an excuse for the NSA to do whatever they want and gives them more leniency with there spying due to the fact that the government may ask for more extra measures.
I believe it is blatantly obvious that the United States is not exactly apologizing for their blanket surveillance programs covered by the NSA. I believe the United States government is unwilling to shut down these programs and wants to avoid talking about them as well. I believe that the US Embassy closures could be a ploy to help get support for the NSA's programs.
Yes, the U.S. Embassy closures are a ploy to harness support for NSA blanket surveillance, because the federal government goes to great lengths to craft public information. The CIA believes that if they can fear the public into thinking that there are credible threats, they will be more accepting of invasive surveillance measures, such as the NSA PRISM program.
Anytime the U.S. makes a move it is usually because they have a bigger plan in store. They almost always know about any event and attack before it happens so that makes it hard to believe that they are worried about terrorists attacking their embassies. They are closing their embassies so that they can do other things unnoticed in that area more than likely. They can also use people's fear to bring more security (NSA) into their lives without objection.
U.S. embassies should be safe, and if there are threats made against American targets then the buildings should be shuttered. It's not about NSA's spying program, it's about safety. However, if the NSA can spy on foreigners without doing so with American citizens, then the National Security Agency should do so in order to save lives.
It would be foolish to believe that the government is capable or caring enough to do something like this to boost the reputation of a failing agency. A more likely cause of the embassy closures would be something along the line of budget cuts to that department, and nothing to do at all with the NSA.
There is no evidence that the closures of US embassies in the Middle East is a ploy to garner support for NSA surveillance. Instead, these closures were meant as preemptive safety measures to protect personnel in the affected regions. If anything, these closures are evidence of the nation's skittish reaction to Benghazi, not to the NSA revelations.