If it's bacterial, can I just dump some sort of antibiotic into the tank once or twice a day?
Is there any possibility with some supplements (like Selcon) and keeping on eye on him that he can fend off a bacterial infection on his own?
Yes, very possible - if what you are dealing with is a gram positive bacterial infection. Gram negatives are much more lethal and almost always require aggressive antibiotic treatment. Unfortunately, it can be very difficult to differentiate between the two without a culture sample under a microscope. Also unfortunate... if this is a gram negative infection he will likely be dead (without treatment) in a day or two.
As a very general rule of thumb, if it's a new fish the likelihood of gram negative increases. With existing/established fish, it's almost always gram positive.
Are there any signs of decline? if he's not doing as well in the AM I will probably go into panic mode and set up a small, cheapo QT.
Really hoping he cut himself on a rock or got into it with a bristle worm last night lol. He's actually a TON more active today than I've seen him any other day since I got him. He's still doing normal goby things, but he was actually fairly open about coming out for food today and didn't seem reluctant to stay out into the open until he was full.