Can an atheist be punished?

Peace be upon the late Rebbe Shlita.
A question occurred to me: Will God punish an atheist on Judgment Day? After all, he is a transgressor according to logic. How is it possible to punish someone because he reached an incorrect conclusion?
It is true that a sinful believer or an atheist who fights religion can be punished, but an atheist alone, right?
By the way, the rabbi knows the midrash that if one wants to know the attributes of God, then one must study an agga. Hence, there is value and positivity in the conclusions that arise from the homily. In my opinion, am I right?
Does the Rabbi see the Sages as having the authority to rule on heavenly matters that are not halakhic?