Yes, pass the background check and buy the gun. You can walk out the store that day with it
You are legally allowed to open carry but I'd advise against it. Philadelphia Police frown on open carry and you will most likely be stopped and they will run a full background check on you. And if you are ok they will give you a lecture on why you shouldn't. If you have a CCW just carry it concealed. You'd be much better off.
Thanks! Your answer is awaiting moderation.