Not possible. Tbe award was not created until 2005.
The award is retro to 2001 and it is awarded to “any soldier”, which would include generals I imagine.
http://www.army.mil/symbols/combatbadges/Action.html
“In 2003, Petraeus, then a major general, commanded the 101st Airborne Division during V Corps’s drive to Baghdad. In a campaign chronicled in detail by Rick Atkinson of the Washington Post’s book In the Company of Soldiers, Petraeus led his division through the battles of Karbala, Hilla, and Najaf (where he came under fire during an ambush by Iraqi paramilitary forces).”
From the Wikipedia link someone had posted in this thread.
As commander of the 101st Airborne, Petraeus saw combat for the first time during the division’s drive up the Euphrates Valley, with sharp firefights in Najaf, Karbala and Hilla. But it was during the division’s subsequent occupation of Mosul and northern Iraq that he won widespread acclaim by resurrecting the local economy, restoring services and preserving order with strategic force, which included killing Saddam Hussein’s two sons. Posters in the division bivouacs read: “What have you done to win Iraqi hearts and minds today?”
http://www.washingtonpost.com/wp-dyn/content/article/2007/01/06/AR2007010601185_pf.html
Incorrect.
http://en.wikipedia.org/wiki/Combat_Action_Badge
The Combat Action Badge (or CAB) is a military badge worn in the U.S. Army. The emblem features both a M9 bayonet and M67 grenade. The Combat Action Badge may be awarded to any soldier after the date of September 18, 2001 performing duties in an area where hostile fire pay or imminent danger pay is authorized, who is personally present and actively engaging or being engaged by the enemy, and performing satisfactorily in accordance with the prescribed rules of
engagement. Award is not limited by one’s branch of service or military occupational specialty, but is only authorized for wear on U.S. Army uniforms. A silver badge 2 inches (5.08cm) in width overall consisting of an oak wreath supporting a rectangle bearing a bayonet surmounting a grenade, all silver. Stars are added at the top to indicate subsequent awards; one star for the second award, two stars for the third award and three stars for the fourth award. In comparison to the Combat Infantryman Badge (CIB), the CAB has a silver rectangle backing rather than blue, and the CAB is 1 inch shorter in length than the CIB.