Does consciousness exist for William James? Why or why not?
Yes, consciousness exists for William James, specifically in his essay "The Will to Believe." So, let's begin with the absolute evidence since that is the answer to your question, and then we can expand upon it.
There is but one indefectibly certain truth, and that is the truth that pyrrhonistic scepticism itself leaves standingly — the truth that the present phenomenon of consciousness exists. That, however, is the bare starting-point of knowledge, the mere admission of stuff to be philosophized about.
In other words, not only does consciousness exist, but it is incredibly important. However, consciousness itself is not the be-all, end-all of philosophical theories. Instead, it is the very first of the building blocks needed to even enter the world of philosophy. As William James says, it is the "bare starting-point of knowledge," and that ultimate philosophical thought and theory are found elsewhere. If you would like to see the quote in context, feel free to read the full essay at the link I provided below. However, for now, let's expand upon it after having explored (and explained) the above quote that forms the basis of the answer to your question.
Now, let me go further by mentioning another work of William James'. In Pragmatism: A New Name for Some Old Ways of Thinking, James begins to explore both philosophy and pychology together. He expands, here, on the concept of truth and says that the idea something is "true" is just the "expedient way" of discerning the world around us. This coined the new concept of "New Relativism" which became THE philosophy of controversy in the 1900s. This idea about truth proves William James' belief that one must go further than consciousness to achieve knowledge and wisdom.
According to William James, the most basic of facts not only about our world but about the universe as a whole have only one way to be valued: if they produce consciousness in humans. If the facts, even those of science, do not produce consciousness, they are useless. In this regard, it is not the idea that one is "good" or "bad" that is important (which is often referred to as subjectivisim). William James asserts that EXPERIENCE (the action leading directly from consciousness) is the main factor. To further this idea, William James believed in a concept called "radical empiricism,” which takes regular empiricism to the extreme. Taking experience as it comes is not enough. One must search for and embrace experience. Experience, then, takes consciousness to a new level of philosophy.
In the context of the entire set of essays, "The Will to Believe" takes on a very positive meaning. The idea can be seen right within the title. William James is showing us that, even though evidence and facts are not there, humans can be in the "right" by clinging to their religious beliefs. James' idea is a reaction to the newer thought of his era that science will be able to eventually explain everything. James rejects this idea and gives great value to human thought and consciousness apart from science. Here is a good excerpt that proves this point:
What do you think of the world? These are the questions with which all must deal as it seems good to them. They are riddles of the Sphinx, and in some way or other we must deal with them. ... In all important transactions of life w have to take a leap in the dark. ... If we decide to leave the riddles unanswered, that is a choice; if we waver in our answer, that, too, is a choice; but whatever choice we make, we make it at our peril. If a man chooses to turn his back altogether on God and the future, no one can prevent him; no one can show beyond reasonable doubt that he is mistaken. If a man thinks otherwise and acts as he thinks, I do not see that any one can prove that he is mistaken. Each must act as he thinks best; and if he is wrong, so much the worse for him.
So as you can see, experience, even in the way that a man acts upon his faith, is the most important idea. William James also rejects complete reliance on logic as the basic for philosophical thought. Why? Here is the answer:
Often enough our faith beforehand in an uncertified result is the only thing that makes the result come true.
The effort of a person to achieve a good sense of morality is enough. There is "rightness" in that and "goodness" in that. People possess free will in that sense. This idea, though, should not lead to "sentimentalism" and a body should still deal with both pessimism and nihilism. According to James, no one philosophical viewpoint can contain all of reality. Because of this idea (as well as others), even those who are avid critics of William James, believe him to be an amazing philosophical mind that is willing to entertain multiple ideas at once.
Finally, I would like to suggest some further reading for you on the concept of consciousness. Why? Because William James had a LOT to say on this subject (and not just in this one essay). I would suggest that, in order to expand your concepts of philosophical thought, you read William James on Consciousness Beyond the Margin. In it, William James explores all of the known theories about human consciousness and continues his ideas on religious experience. This book would be a perfect follow-up reading after adequately answering your consciousness question.