No those who do not hearken to God do not have faith because Faith originates with the assurances of the Testifier. Those assurances are the substance upon which Faith stands and without those assurances all that one has is unsubstantiated speculation no matter how strongly convinced is the person who believes the unsubstantiated.
The things which God assures us are true are called ὑπόστασις (hypostasis)
Those assurances produce ἔλεγχος (elegchos)
ἔστιν δὲ πίστις ἐλπιζομένων ὑπόστασις πραγμάτων ἔλεγχος οὐ βλεπομένων
Another way of saying the same thing is when Paul said "Faith comes by hearing and hearing by the word of God."
If God did not say it first, then a conviction is not faith.
Still another example is when Jude wrote that Faith was delivered. God's word is the origin of faith.
ἅπαξ παραδοθείσῃ τοῖς ἁγίοις πίστει
Agnostics and Atheists believe in things for which they have no true evidence but their belief is not faith because it is not predicated on the trustworthiness of the One who testifies.
ἐκ πίστεως εἰς πίστιν