There's a few things to point out.

On the one hand, the President has repeatedly asserted he doesn't like leakers.

On the other hand, we're being told to believe that if Q was a threat, the government would go on some campaign against an "unknown" (Q) individual like they did with Snowden. Q, hasn't leaked any classified documents, hasn't bombed any buildings or caused mass casualties - all of these things are cause for someone to go after an anonymous individual publicly. Then there's the stuff clamhurt_legbeard mentioned.

But then on my third hand, because I guess I'm some mutant freak, I wouldn't put it past any spook to operate out in the open.

At the end of the day, this post looks like a distraction. The whole premise relies on the fact on some manhunt on "Q" being a very public thing. A public manhunt doesn't need to be a thing because nothing has happened from "Q's" end to necessitate one.