I think a persons answer to the question of God's existence is the foundation of any moral philosophy.
Does that mean if any given philosopher doesn't express belief in God they are engaged in 'immoral and/or ammoral' philosophy?
That does have a certain logical consistency about it.
I'm okay with ammoral philosophy. From the perspective of a believer, most philosophy certainly is either immoral or ammoral (and occasionally both).
It has framed the philosophy of most, if not all philosophers. Nietzsche, Schopenhauer, Descartes, or any other philosopher discussing morality must first answer 'the big one'...
Yes, it certainly follows that any given philosopher's view of the 'God question' is going to color or influence their 'philosophizing' about everything else. Philosophy is a human art after all.
That being said, the serious study of philosophy requires that one drop all pre-conceived notions and follow only that which is dictated by logic, reason and physical evidence. This is the essential definition of the 'art' of philosophy itself. And given that all religions are fundamentally based on 'faith', the study of philosophy is generally, but inherently, biased in favor of those who do not have a strong or pre-determined religious faith.
This does not preclude faith in 'deist-type' (or agnostic) views of God as some ambient unknown entity. This can be compatible with the relativist (non-absolute) position in epistemology. It is only the 'strong theist' type who will have 'issues' with the question of epistemology. For many potential students of philosophy, this is a 'red-line issue' that often precludes further advanced study (though some 'Jesuit-trained theist' types can surmount this obstacle - I have great respect for this type of argument and those who can make it).
Epistemology consists of asking the questions - what is truth? or what is knowledge? (all the variations of these closely related questions). This would be the 'ground-zero' of philosophy. The question of God's existence is actually secondary or subsidiary to this one.
As for the particular philosophers that you mention, it is my opinion that Nietzsche was probably one of the most spiritually-inclined of all philosophers - I believe that he genuinely mourned the death of God and it is this that defines his subsequent yearning for a replacement (and celebration when he thinks he finds it).
As for Descartes, he certainly was an ardent Christian theist. However, with his religious zeal to create the perfect rationalization of God ended up creating a couple of the most powerful intellectual tools of atheism ('cogito ergo sum' as well as the principle of 'radical doubt').
As for Schopenhauer, I've not studied his work as extensively as I have many others. I don't know off hand if he was a genuine Christian or not, but from what I have read of Schopenhauer, he certainly comes across as a typical 'deist' type with his noted passion for the primacy of aesthetics and the idea of 'will'.
As for the other 'big names' of philosophy - strong deists and mild deists seem to be the majority of philosophers, with more than a few atheists as time goes on. Christain philosophers are certainly evident in earlier times (Augustine & Aquinas being two of the most impressive ones), but since the 17th century, I see little evidence of anything but deism (and increasing atheism) amongst 'big name' philosophers.
If God exists, then all debate about God is absurd (and blasphemous). If God doesn't exist, then all debate about God is absurd (and a waste of time). I don't see any way out of this dichotomy.
I don't see how you have established a dichotomy.
If there is no God, why does it matter that you have wasted your time? Shadows and dust right? Why does anything matter? On the other hand, if there is a God, why shouldn't we discuss his existence if that is in doubt?
It is a dichotomy since there is only two choices available. Either God exists or God does not exist.
If there is no God, then arguing/discussing it is mere entertainment or sophistry. You are welcome to do it, but it isn't very interesting to me from a philosophic perspective. It looks more like 'mental masturbation'.

Btw, atheism does not equal nihilism. I will defend that position most vehmently if challenged.
Now if God really does exist, then discussions about whether or not God exists are essentially blasphemous - or entirely a matter of personal conscience. Again, there's nothing about such a discussion that warrants philosophic interest.
If you want to rephrase the question in terms of epistemology, then you will have the interest of every genuine philosopher.
If you start with God, all philosophy is moot and superfluous. You have your bible, what more do you need?
It does not make philosophy moot or superfluous. However, it provides an alternative frame for the picture that is philosophy. Philosophy is the search for truth. Is it true that a God exists or isn't it?
Search for truth? You are presuming that such a thing exists? That's not philosophy - that's religion.
Philosophy is a love of wisdom (philo-sophia, from the greek)
You assume I am a Christian, and a naive one at that.
Please cite. I've made no such assumptions. Your religion (or lack thereof) is technically irrelevant to me.
My expression of "you have your Bible, what more do you need" was phrased in a sloppy way. My statement is meant to be generic. Any believer has a holy book and if they are a true believer, then that's all the philosophy they need. Everything else in philosophy is just going to lead to blasphemy or a test of faith.
That is to say, all religions constitute specific philosophies in themselves. Christian or Muslim doctrine are both comprehensive philosophic systems that do not admit of any alternative philosophic interpretations.
What if I'm a Muslim or a Mormon? Please refrain from such bitter and presumptuous comments. They make you less credible and make this conversation much less interesting to me. I would very much like to understand the athiest position. Perhaps its nothing more than anger towards theists in your case, friend, which makes me less inclined to learn from you...
You are perhaps demonstrating here why those who hold to any given religion find discussion of most western or modern philosophy to be rather challenging. Again, I make no assumption or inference here about your religious status. I am addressing these issues in a philosophically objective manner.
And since you are making inferences about my views on religion (unwarranted I might add), I will state that I am most certainly am not anti-religious. I go to great lengths to defend the essential religious position and I've long argued in defense of religion's right to fully participate in civil society and politics. But
I will not give an inch in any serious philosophic discussion to any religious notions. They have no standing at all in the general study of philosophy. Thus, if one holds strongly to any particular religious position, then all philosophic discussions are necessarily interpreted in the terms of that religon.
All subsequent philosophies should be based on the answer to the question 'is there a God?' Descartes was right...
Subsequent philosophies?
Descartes was right about what?
(Btw, Descartes was quite properly named by Pope John Paul II as the 'father of atheism', though that certainly wasn't Descartes' intent).
Its true that Descartes' philosophy opened a huge can of relative worms. It would seem that Darwin, a Christian, also chipped in. So what? Aren't we better off with honest inquiry?
Yes, honest inquiry is always good - this is a fundamental premise of classical liberalism and that's the only 'philosophy' that I do generally follow.
But my point is that Descartes and Darwin as well would probably have a heart attack (if they were alive today) if they knew that their studies formed strong arguments favored by atheists. Both men were genuine and honest Christians to the best of my knowledge. That is to say, honest philosophical inquiry by honest Christians tends to produce things that are un-Christian.
William of Ockham is another famous Christian intellectual who has, with his honest faith in God, has contributed another powerful argument favored by atheists and agnostics alike - Occam's Razor.
As for why Ockham's Razor is generally called Occam's Razor is a mystery worthy of a Ph.D. dissertation!