Yes, we struggle with the flesh for certain. I believe the natural man in 2 Corinthians 2 is speaking of the unregenerate man.
I don't see where whether he believed in a spiritual God question is valid in this case brother, as far as your argument is concerned, though it is a worthy point to be discussed.
I believe it is obvious he believed in spiritual matters and God to some extent as well although it appeared his faith was misplaced. Do not even the lost fear God, believing he exists, fear hell, fear falling into the hands of a just God, and can even express said fear, though unrepentant?
Here is John Gill on the matter of the text:
For I perceive that thou art in the gall of bitterness,.... Alluding to Deu_29:18 with which compare Heb_12:15 and signifying, that he was in a state of nature and unregeneracy; under the power and dominion of covetousness, ambition, and hypocrisy; and in a way pernicious to himself, infectious to others, and ungrateful to God, and to good men; and that instead of the root of the matter, the truth of grace being in him, there was nothing in him but the bitter root of sin; which bore gall and wormwood, and everything that was nauseous and disagreeable:
and in the bond of iniquity; referring to Pro_5:22 and suggesting, that he was held fast bound in the bonds of sin, and with the cords of iniquity, or was entirely under the government of his lusts: the preposition εις, which we render "in", may retain here, as is by some observed, its proper sense of "for", or "into"; and have the same signification it has in Heb_1:5 "I will be to him for a father", or "a father", and "he shall be to me for a son", or "a son": and then the sense of Peter is, I plainly perceive and clearly see by thy words and actions, that thou art nothing else but a lump of bitter gall, and a bundle of sin and wickedness.