if you would like to create a platform on which a token represents the value you place on an answer to a question, the question is asked, someone answers correctly, the token is transferred to them, and the person who answered the question would then like to "cash out" so to speak. In order to "cash out" on this token and convert it to bitcoin, is it necessary to have previously held an ICO in order for that token to hold any value in relation to Bitcoin?
Well if i understand you correctly, you are trying to ask if you can create a token that you can use to reward people for answering quiz? Left to me i'd say yes, people love free things and I've seen projects emerged as a charity foundation to reward community and they got successful.
Even in real life, there are nonprofit foundation doing such things of setting educative quiz for people in order to reward them, i think it's possible too on Blockchain and i believe the concept will be very much welcome and adopted by the community