Possibly.
But I doubt it.
Seems more plausible than a faked coup.
From my reading of history the only fake coup I've ever heard of was the business plot against FDR which was invented by FDR to given him leeway in implementing his agenda and it didn't involve actual military action. No sane ruler would chance triggering a fake coup involving bombs, military action, and him flying around trying to escape. There's just too much of a chance it might become a real coup.
Believing that Erdogan faked a coup with zero evidence, zero historical precedence, and ignoring the obvious reasons the military had to coup him(A list of people he planned to purge) is Arab level conspiracy thinking. Not the kind of stuff I'd expect Americans to be engaging in.