No, because they would be members of the Iraqi military, secret police, and/or political leadership.
The scheme could be elaborated for extra security easily enough, e.g. by distributing the "launch codes" among multiple, independent people. You can play with scenarios like that -- say maybe five out of ten people have to send their codes for the whole thing to work, or whatever. But that's probably being too anal about it. I just don't think it's that big a problem. You don't get to be a dictator without solving this kind of carrot/stick problem all the time -- otherwise your own security guards would do you in long before you came to power.
Again, control problems were no obstacle to the acquisition of doomsday deterrents by the US, Russia, China, Britain, France, India, Pakistan and Israel. It only takes about five minutes to figure out "good enough" solutions to the problems involved, once you set your mind to it.