No, the people who tell the Obama administration what to do, told the media to make a circus out of the case.
I can't tell if you actually believe this or if it's just sarcasm.
It's highly unlikely that anything about the Zimmerman trial was a deliberate ploy to distract the American public from more pressing issues but... The president did explicitly weigh in on the trial which gave it more notoriety in the press. It's not impossible that he was hoping it would distract from the NSA issue.
More likely though, there are just more people for whom race relations is a bigger deal than government spying.