You're assuming any new information is gained. That's entirely hypothetical and can't be treated as a concrete truth.
Does 2+2=5? I could spend the next twenty years asking myself that question, and sure, I MIGHT stumble upon some mathematical breakthrough that has nothing to do with the original question, but if I'm going to spend 20 years dedicated to something, my expectation should be to answer the original question.
So if your expectation is fruitless to begin with, then you're starting a venture knowing that you're trying to solve a question that has no answer. You could apply that to any waste of time. If Albert Einstein had found the inspiration for the theory of relativity while watching paint dry, would that mean that the intro to theoretical physics would involve a three hour session of watching paint dry?
Happy accidents happen, but we shouldn't plan for them. That's called inefficiency.