I think it is impossible not to apply logic to Naruto. "Logic" is any particular mode of reasoning. We attempt to reason, make sense of, categorize, understand, comprehend, figure out, and know whats going on. Logic gives us labels for the unknown, so we can make sense of it. If you have an understanding of Naruto, such as it being a "Shounen Manga" this is your own Logic- even if it is a seemingly universal label.
The story of Naruto delves into this aspect of human nature. Characters are all trying to figure out how to REALLY know each other, to live in harmony, etc. Can we TRULY know each other NOT LOGICALLY (not to be confused with illogically), despite the NECESSARY requirement to label and understand each other intellectually?