Can fallacious detecting mode hamper creativity?

Yes, it can. I cannot recall the exact research, but I have come across much research over the years that suggest analytical thinking does hamper creative thinking. From a neuroscientific point of view this makes sense given that our frontal lobes (where analytical thinking takes place) are shut down when we dream, and that moments of insight often hit us in altered states of consciousness, like waking up or falling asleep.

...if fallacious reasoning were to spark of an idea, leading to another idea or part of the solution to the big picture, would it be wrong?

The "wrongness" of the conclusion needs to be judged based on the conclusion itself, not the process in which the conclusion was reached. The reasoning could be fallacious, but the conclusion still correct. This would be like saying that we should not smoke if we want to avoid lung cancer, because a fairy told me. If we call "talking with fairies" our "creative process," we are incorrectly relying on a flawed method for determining empirical facts. Other creative processes can be very effective in problem solving where there is an objective answer, but this gets into a new area that extends outside the scope of your question.