Sounds like chances are remote to get the same day Oath. :-(
Yeah, if you assume the office as a whole closes at 4:00p, then your 2:00p interview appointment just doesn't give them enough time to process your naturalization certificate after the interview approval. They have to manually paste your photo on the certificate, quality-check it, etc.
So if you assume that there is an oath ceremony at 3:00p (I don't know if there is), then they will ask you to report for it at 2:00p downstairs. There they will make sure they have your naturalization certificate correctly prepared and ready to hand out as soon as you have taken the oath. So if your interview is at 2:00p, it is hard to see how you would be able to get a same-day oath unless the office closes a lot later than 4:00p. If the oath ceremony is at 2:00p, then you're definitely out of luck for same-day processing.
Good luck either way - I am sure your oath scheduling should not to be too far behind the interview approval.