I think that's part of it, at least for some Koans. I'm not a Zen practitioner myself (though I am a Buddhist) but I think its methods are intended to guide the student towards a direct experience of enlightened mind (satori).
Koans are not usually posed in isolation. Instead, the teacher will assign the koan as a meditation object that the student will contemplate for weeks or months. Periodically the teacher will examine the student to see if their understanding has sufficiently progressed. If not, they're sent back to the zendo. Koan practice seems to involve pulling the rug out from under the student again and again, so that they begin to see the limitations of not only binary thinking, but of all concepts. It produces satori by ruthlessly stripping away everything that is not satori.
Indeed, I think a Zen master would be somewhat amused by this whole thread, because getting to a rational understanding of a koan (or koans in general) is about as far from the point as one can possibly get.
Zen and Buddhism have the same fundamental goals and strategies, which is what you would expect given that Zen is a school of Buddhism. Ideally everyone would get a direct experience of satori every time they encountered a Zen saying (or wouldn't even need the Zen sayings to experience satori!). However different people are mired in various attachments to different degrees, so it would only be a small minority of people who would directly experience satori from encountering a koan. Still, even if a koan does not directly and immediately lead to satori, it can help bring a person closer to that stage where they do experience satori later on.
Because they are riddles with a complex conceptual structure, koans as meditative objects are qualitatively different from relatively simple meditation objects such as the breath. By virtue of their conceptual and intellectual nature, koans can help guide a mind toward satori by utilizing the mind's inclination to ponder rather than going directly against it (as meditating on the breath often does). In this process the mind may think up all sorts of contemplations about the koan, but sooner or later the mind either lets go of trying to think up a satisfactory answer or it thinks up an answer which paradoxically highlights the ultimate futility of attachment to conceptual thinking. Imo those who directly and immediately experience satori when they encounter a koan just go through this process extremely rapidly (everything just "clicks" into place) because the inclination and previous conditioning of their minds makes them ripe for satori.