There are two good answers to the question above: no and yes.
First, for the no. If you are not a competent critical thinker, I would suggest you not pursue it. If, like much of our culture, you hear with your eyes and think with your feelings, then you will be in trouble. The following warning by Mark Noll and David Wells (1988) gets right to the point.
[The] journey from Word to world is fraught with peril even as it is ripe with potential. Bridges built between God's Word and our world are susceptible of carrying traffic in both directions . . . most of the traffic has been moving in the wrong direction. Twentieth-century people have allowed the cognitive constraints and the psychological conventions of our own day to limit what the Bible may say. This reverses the proper situation. It is the Bible that deserves to prescribe the cognitive horizon for the twentieth century, just as it has been for every century.
Which leads to the second point: If you are biblically and theologically anemic, I would not suggest you pursue PhD work outside Christian institutions. Everybody leans on what they know best. So if your understanding of people, problems, and change is deep and wide in the secular rudiments of the psyche but weak and thin in the faith once for all delivered to you and the rest of the saints, then you will be in trouble. You will function more as a psychologist who happens to be Christian than a Christian who happens to be a psychologist. The academic and professional guilds are persuasive when you function under their presuppositions rather than God's, and powerful when they hold over your head a degree, a license, and a paycheck. Be careful.
If you have a PhD in psychology, counseling, or social work and a "Sunday school degree" in Bible and theology, anybody can guess what will exercise the greatest influence in your work. Prior training in biblical counseling, especially a developed theistic epistemology and biblical psychology, is a minimal prerequisite. Even better would be a seminary degree.
Finally, I would not suggest PhD work outside Christian institutions if you do not have sharp dialogue partners to accompany you on your trek. After I completed graduate school in clinical psychology and attempted to practice as a Christian, I sensed the spiritually vapid nature of my work. God used David Powlison and Sid Galloway as mentors to help me develop a more biblical perspective. They gave me their time and energy---countless conversations, helpful responses to my many "yes, but what about" questions, and many thoughtful e-mails.
But here's when I would say "yes": if you can think and live like a missionary. Missionaries enter into another culture both as learners, and with time, as teachers. They are motivated by love and therefore move toward the culture with a measure of acceptance; they are moved by the mission of God and therefore possess a distinctively divine agenda. Our psychology and our counsel is messianic and revolutionary. There is good reason from our perspective as Christians to view the mental health subculture as a mission field, or at least as a kind of unreached people group. The gospel's psychology subverts the foundational narratives and metaphysical, epistemological, and anthropological presuppositions of the secular psychologies. We don't just offer up junior versions of their non-Christian systems. The secular psychotherapies desperately need redemption, not because they are all wrong, but because they are fundamentally wrong about the most important things.
Our goal, then, should not be simply to obtain a seat at the psychological table, but instead to invite diners in the Mental Health Café to a banquet feast with fare beyond their wildest dreams: a Chef who offers living bread and living water and even life beyond this one. Would not a retooling of C. S. Lewis's inimitable challenge in The Weight of Glory be apropos?
We are half-hearted counselors, fooling about with Freud and Rogers and Beck when infinite joy is offered us by Another Counselor, like an ignorant child who wants to go on making mud pies in a slum because he cannot imagine what is meant by the offer of a holiday at the sea. We are far too easily pleased (modified from Lewis, 1980, pp. 3-4).