Crediting Authors who are not Cited in an Article but have influenced it using Chicago Author-Date System in the Humanities
This question hinges on the relevancy of citing this additional source. Whether or not it is appropriate to cite the work depends on the scope of its influence on your work.
For example, if you use a methodology or structure in your paper that is unique to a certain work, you should cite this. As per Chicago guidelines, you would cite the author and year without a specific page number (unless relevant sections are distinct).
However, if you write a humanities paper on new age magic because you were inspired by Harry Potter, this is not appropriate. Even if you otherwise would not have conducted your research without having read Harry Potter, it is completely irrelevant to the paper.
It is tempting to recount the path you take researching a subject when you are writing about it, however this is rarely relevant to your thesis. Cite work when credit is due, otherwise leave it out or use a formal acknowledgement.