If a person has a faith-based belief, and if faith is beyond reason, then is that belief outside the reach of reason?
This is a really well-worded set of questions. I'd like to take a stab at this for my own mind.
What I'd say is that the nature of the belief, if it is inspired by faith, is not the same kind of belief as believing things in the mundane sense of the word. If it is faith, it is looking to the ineffable to begin with, which is beyond being able to be cataloged and indexed along with everything else in the mundane world of daily doings.
What sort of faith-based belief that I would see, would have to do with the 'big questions' of life, being, meaning, and existential purpose. Faith reaches to God. What beliefs arise from that, will generally center around insight and revelation, things which are not invested or accomplished through the facilities of reason and logic.
So yes, that belief is 'beyond' reason, but I would not say it is outside of its acknowledgement, and certainly not in violation of it. Rather it's a partnership, where each has its uses and strengths to yield to the other. They harmonize and complement. But when one operates without the other, reason without faith, or faith without reason, pretty soon we become unbalanced with the world, and we suffer.
Can that person effectively engage their faith-based beliefs with reason?
To clarify from above, I would never acknowledge belief statements, like evolution is wrong, to be "faith-based". That's not faith in the religious sense of the word. That's not an impulse to the Divine, which is which what a spiritual or religious faith is. That's an assertion of the mind in ignorance and fear, and an abuse of the word faith as a bypass for reason. Spiritual insights are not about scientific truths. They are not about facts and figures. They are about the nature of existence holistically, not technically.
So then to answer this question, yes, certainly. If they are being true to faith, they must be true to reason. Reason cannot let you experience the human body. You need to get up and move around and experience it for that. In this sense, the experience of the body itself, is beyond reason. But reason lives well with the knowledge of the body, which only came through the body itself. It's the same thing with the spiritual body in us. Not really different, actually. Just different aspects of the whole being. Different ways of knowing and knowledge, and living together as a whole.
Can someone else effectively engage their faith-based beliefs in rational conversation? Or is faith and reason simply oil and water?
Yes, certainly. I am right now.