No, because God decided that to kill (or, perhaps more specifically, murder) is wrong. Murder is killing someone who is not an immediate threat to self or others. If God is all powerful, then by definition, no one is a threat to him, and therefore any killing that he does would, again by definition, be murder, which he has specifically forbidden. The rule setter has no right to set aside the rules only for themselves. A Judge was recently investigated because he had gone into the Court system to dismiss his own moving violations. This is obviously not acceptable, since, as a Judge, he has a special authority to enforce the law, and I think it in fact warrants a higher standard of accountability. There's no room to say “Well, he couldn't have known any better.” Therefore, I am not able to accept an argument that states that God is above his own laws. That would be like the President smoking marijuana in the oval office, while simultaneously approving raids against medical marijuana facilities. He would have no right to do so. We would consider such behavior contradictory, hypocritical, and unjust. We would never want to allow a person of such a status to be above the laws that they create and rigidly enforced. If God does something in spite of having declared it wrong, then it was either bad advice, or a wicked action. I see no other options.
So, as you can see, I think that God most certainly does not have a "right" to kill. In regards to whether God could go without killing, I think it is relevant to his right to kill. I'll explain. One might say that God could justifiably kill to protect others, in other words not murder, but the problem I encounter with that is that, being all powerful, he has an infinite number of options available to reach a non-violent solution to the problem. Humans have limitations that in many cases could make killing another person to protect someone else justified, simply because a person has no other options. For example, police may have no choice but to kill someone who is shooting up a school, in order to protect the lives of the students, staff and community. This is not the case for God, and it would honestly be nice to see him shower an enemy army with adorable kittens, laughing gas, Hostess Cupcakes, or something more humane than just death in order to prevent them from doing evil. It should not be necessary for God to do evil in order to prevent it. That is a limitation that people have. The fact that God has this very human limitation, when not having it should be his most defining and recognizable characteristic as a benevolent and loving God, as well as choosing to destroy his (followers) enemies, who can not possibly be a threat to him personally, leads me to believe that he is in fact, man made.