Does one who says, "God knows I will not commit this sin," while being truthful at the time, but then is overcome by his soul and commits it, become an unbeliever, given his awareness of the scholars' disagreement regarding one who says "God knows" while being a liar?

The statement "Allah knows best" (يعلم الله) is not an act of disbelief (kufr). Jurists have differed regarding the necessity of expiation (kaffara) for it; some consider expiation to be recommended as a precautionary measure, while others deem it obligatory if it was intended as an oath, otherwise not.