No, they wouldn't. For one thing, there really wasn't a star fleet bad guy in the movie. Just your typical well meaning but completely mislead admiral that we've seen many, many times. .
Erm, I don't recall any other admiral willing to slaughter other starfleet officers let alone start an interplanetary war by bombing an alien world. Just me?
Fleet Admiral Cartwright comes close - using the Klingons as proxy.
Although saying Admirals on Star Trek have been world-bombing, Startfleet-slaughtering berzekers is hyperbolic, it merely exaggerates the well-known effect of Star Trek Admirals and other ranks above Captain going rogue. Star Trek Into Darkness continues the cliche. They are becoming much akin to Red Shirts.