This is a good strategy and as was addressed in my thread, microing your placements can make a huge difference. I have had one three illuminators clear a desert planet (the one without kodiaks of course). One illuminator can easily defeat three LRM's if maneuvered properly. The primary reason for this is the side cannons and the damage distribution that effects mitigation less.
As far as the Kol goes, yes it is awesome. You can just throw it into the middle of the first few worlds you find and win without any trouble.
(Oh and for the record, Marzas are best once you have to actually go to war. That is once you hit a contested world and actually start fighting an opponent rather than just militia. Kols are the best to begin with while Marzas are the best second one with Dunovs after that.)