For me, the yes is resounding and self-evident. The most obvious point, of course, is that it would be impossible not to. We use our minds every time we read the bible, listen to a sermon, or have a conversation. Without out the use of our intellect we would have no basis to process or interpret anything we hear. When I hear people say "we can't know that with our natural mind" I sometimes hear it as "don't question, test, or try to figure that out." I don't think that response is ever recommended in history, scripture, or by any truly great thinkers of whom I am aware.
What possible benefits could be served by turning off our probing, questioning, skeptical, imperfect minds?
Is God the author of all Truth? I believe God is. Does that fundamental, cosmic, universal capital-T-Truth ever contradict truth in science, math, etc? Assuming the mathematical/scientific truth in question is true, and not human error (as in a flat earth, the four humours, et c) I believe the answer to be no. If we believe that the truer something is, the closer to God's perspective it is, then searching for truth and Truth is a very, very good thing to do. If we really believe that God is all-powerful, and behind every real truth, why would we hesitate to question, learn, and test? Is a fear of questions an indication of great faith, or little, fragile faith? Sometimes, to be sure, our human minds misinterpret, our technology fails, and we end up with misconceptions of epic proportions. But continuing to learn and grow in knowledge and wisdom of all sorts will mitigate such failures far faster than shutting down growth because we fear to fail again. We are created in the image of God. This includes our mind. While we are flawed because of sin, we still reflect Divine glory and creativity. Our logic and reason, though they may be flawed at times, are still a reflection of God's design. Logical equations that we observe to be true are not in conflict with God's design- quite the reverse!
Look at history- how have the great advances in human learning and achievement, both sacred and secular, come about? Did Newton experiment and quantify basic physics from scriptural revelation? No, though to the degree that his observations and conclusions were correct they never contradicted scripture. Not to say that spiritual revelation was never involved (Luther, anyone?) but it certainly wasn't limited to that.
The Bible was written to show us the heart of God and lead us to Christ and to holiness, love, justice, mercy, and humility. The Bible wasn't written as a science, math, or history textbook. This does not mean that the Bible has errors in those areas, but that it is not the conclusive, exhaustive repository of all knowledge. Does it contain everything necessary for salvation and holiness? Yes. Does it contain everything humanity needs to continue to develop and thrive? No. Even for the holiness, justice, et c the Bible very often offers general principles instead of specifics. Specifics change with time, location and culture; general principles like "love your neighbor" and "act justly" do not.
Sometimes, human thought and wisdom is misguided and erroneous. In that case, it is antithetical to truth or Truth. Many times, though, human thought is separated from God's wisdom not as an antithetical, opposite altogether-different concept, but by degrees. Humans know that gravity exists, though we cannot explain it fully. God knows the ends and outs of it as a potter knows his vases. Does this mean that human wisdom in this area is wrong? So far as we know, no. It is incomplete. There is a difference. When human wisdom is wrong, and thus antithetical to God's truth, the truth will out. The more we learn, and the clearer our "glass, darkly" becomes, the more we change our conclusions to fit with our increasing data and understanding, the less antithetical to Divine wisdom our wisdom becomes. When our wisdom is true as far as it goes, but incomplete (arguably, there will always be areas of incompleteness until Christ comes and we know all) the solution is the same- we learn, we experiment, we probe, we test. In so doing, we grow by degrees ever closer to truth and Truth.
Sometimes we see, hear, and experience things that we do not understand. There are still so many mysteries to ourselves, our world, and our God that we have yet to uncover. This is where Faith comes in- Faith, the substance of things hoped for and the evidence of things not seen. Sometimes we do not have evidence or conclusive-enough data for an idea or decision. So, we believe what we decide to believe, what the Holy Spirit whispers in our hearts, or what is most congruent with other, better substantiated beliefs. However- is it wrong to continue to study and learn, through natural means, things that we have long taken on faith? Of course not. Seeing the natural realities behind what we hold in faith can only make it stronger. And, if our discoveries contradict that faith, to reexamine is not to hold in contempt. Again- if we really believe that God is the author of Truth, then we must believe that the closer to truth we are, the closer to the heart of God we are. Being willing to change, adapt, and let discovered truth overrule tradition is not evil, and it is not weak.
On Bible interpretation, specifically- which is better: to hold tradition with prejudice above all, or to examine with every light we have the truth of the matter? I'd say the latter, most definitely. While I believe that the Bible is the inspired word of God, I do not believe that any one translation or interpretation is. With no evidence to the contrary, I do not malign the giving of prejudice to precedent. However, we would be foolish to spurn anything that aids us in discovering the original message and Word contained in the Bible.
Imagine being handed a letter. The letter was not written for you specifically, but the bearer tells you that there is great love, great truth, and great knowledge contained in the letter. How would you read it? Suppose the writer admonished some person in the letter to do something. Would you automatically assume that that admonition meant that you should do that, without any inquiry or context? I would hope not. You would try to find out who wrote the letter, to whom it was written, and what their situations were. The same phrase can be written by two different people in different contexts, and, while equally true, mean very different things.
Is it disrespectful to the Bible to study its context, history, and authors? Certainly not. In fact, I think that to neglect anything but a cursory reading of the plain text can miss out on much truth, and can in some cases distort it. If the Bible is to be our rule of faith and practice, and I believe it is, then it deserves every effort at truthful interpretation and discovery we can give it.
To attempt to use the mind without the spirit, or the spirit without the mind, robs us of truth and knowledge. The two should be inseparable. I'm reminded of Paul, speaking of prayer and praying in tongues- 1Co 14:13-17 For this reason, let the man who has the power of using tongues make request that he may, at the same time, be able to give the sense. For if I make use of tongues in my prayers, my spirit makes the prayer, but not my mind. What then? let my prayer be from the spirit, and equally from the mind; let my song be from the spirit, and equally from mind. For if you give a blessing with the spirit, how will the man who has no knowledge say, So be it, after your prayer, seeing that he has not taken in what you are saying? For your giving of the blessing is certainly well done, but of no profit to the man without knowledge.