Yes, I agree with Muman and Edu on the matter. A Jewish man who has a non-Jewish child with a Goya is as if he were not the father at all.
If the child chooses to convert, he is not turned away because he is Zera Yisrael BUT upon completing the conversion, the child is still NOT the spiritual son of the Cohen, instead he becomes the spiritual son of Avraham Avinu. I guess legally, the child would inherit the father's "cohen" last name but would not be Halachicaly a Cohen, not even a Chalal Cohen.