Doesn't the US president also have unchecked authority to nuke any place on earth?
There are of course consequences in that the US may then get nuked in retaliation, but that doesn't stop the actual nuking.
Whether in reality, the orders will be followed (initially the secretary of defense, whose job is to authenticate the order came from the president, and then the joint chiefs they orders are relayed to), or if they would be delayed enough to invoke the 25th amendment and remove the president from power, is a matter of speculation.