I would echo several others on this post and would give my initial assessment as genuine, albeit with a corroded and worn obverse, and a rather curious style (which should not immediately condemn it as a fake, as this coinage was imitated contemporarily in Arabia and likely elsewhere). From the reverse picture it seems like the metal is ancient - there are no casting bubbles and the coin looks struck rather than pressed. However, I will defer to the real experts - there are a few members of this forum who collect Athens as a specialty - who would be able to better weigh in here.
For what is worth, here's a drachm that's in the mail. This coin demonstrates the wide variation that can be encountered with this type. I actually think it is an imitation, probably somewhere in the ancient Levant. 4.2 grams, with earthen deposits
I don't see anything suspicious. Drachms are usually porous, however, I can't recall ever seeing pitting, but that's perhaps because such examples might not make it to the auctions I follow. The owl looks strange because of a die shift resulting in what you see. The style is actually quite nice but it looks crude because of the problematic strike. I think it could be a die match or at least pretty close to this one:
IMHO the best result you could hope to get is VF strike 3/5 surface 2/5, and in terms of value the coin is below 200$ so I don't think grading would offer you anything advantageous
That's a really beautiful coin, definitely a cut or two above what is normally encountered. Did your coin come out of an auction?