The only way you can argue effectively against logic is with logic, so to make a good argument against the notion that logic is omnipotent, you
would have to prove yourself wrong in the process. Without logic, nothing would make sense. Logic is the only way to make a good argument. Logic is what makes a genius a genius. Of course it is omnipotent.
Reality is logic - and part of that logic is the aspect of being fooled into believing that it isn't. If a global standstill took place, the logic of what should happen afterwards would never change, same as it wouldn't were the United States to come to an end.
Logic is not even real. There is pattern and change within life but our failure to attach a logical norm to it means that we have been barking up the wrong tree. We are now convinced that there is a bone in a bird's nest up there somewhere. We feel that we will bark it down eventually. Life as a human within life must be intuitive and to effect this there must be total absorption and immersion within a natural 'not logical' existence.
Omnipotence is the ability to do anything without restriction, logic is the use of cognitive reasoning and observation to make rational predictions, conclusions etc. So how can "logic," which is an abstract concept borne of the human mind, be omnipotent? That's like saying that the smell of oranges can build highchairs. The concept of omnipotence itself is paradoxical, since nothing can do everything. For example, pretend that I claim to be omnipotent. Can I build a box that I can't open? As you can see omnipotence as defined in the dictionary is impossible.
The concept of Omnipotent gives rise to logical fallacy. For example, can an Omnipotent being can create a rock that he himself can not lift. If he can make such a rock then he ceases to be omnipotent and if he can not create such a rock then he is not Omnipotent. Therefore, I conclude that Omnipotent is a logical fallacy and hence Logic can not be Omnipotent.