My experience within evangelical/fundamentalism tells me that they are not. They will often claim to be willing to follow the evidence wherever it leads but in reality they are not. They have determined that the Bible is the literal Word of God and therefore nothing that contradicts it can possibly be true. This was illustrated in a previous post in which William Craig admitted that no evidence could possibly disconfirm his faith because he has the "witness of the Spirit" in his heart.
When I was at Bob Jones University, there were two incidents in particular that awoke me to the fact that honest scholarship was not allowed in evangelicalism.
First, around 1980 a book came out entitled: Decision Making and the Will of God by Gary Friesen. Friesen argued that the traditional view that God has a perfect will for your life including whom you should marry, where you should go to school, what occupation you should choose, etc. was really not biblical. He argued that the will of God in the Scripture only had to do with moral issues and that non-moral issues could be decided by Christians using wisdom (i.e., applying biblical principles).
At the time, I thought that Friesen was right about what the Scriptures taught. However, the administration at Bob Jones Univ. did not. They had taught for years that God has a perfect will for you life. One day after class, I asked Stewart Custer if he had read the book. He said, "No, but I need to read it because Dr. Bob has asked me to write a refutation of it." I was flabberghasted. I thought to myself, that is not being intellecutally honest. You are going to read the book with your mind already made up.
Second, around 1986, Bob Jones, Jr. called John MacArthur a heretic because John was teaching that it was the death of Christ that saves not his literal blood. Even though John graciously clarified his position for BJU, they would not accept it. In 1988, I wrote an article in the Calvary Theological Journal in which I basically agreed with MacArthur. Virtually all of the Bible faculty at BJU agreed with my position but were ordered by Bob, Jr. not to address the issue. They were not to address it in class nor in correspondence.
While these two examples may appear extreme, I think they illustrate the fact that evangelicalism does not allow free inquiry.