It is possible to do the morning dive, maybe not allowed per the rules. You'd need lights. However people have been sleeping on the beach so I sometimes take the chance.
Sunday is going to be crazy at the park. Yes, you could do it, but you won't find me there in the afternoon/evening.
If anyone here is diving BHB this weekend, my advice is to avoid spending much time in front of the beach on the west side in shallow water. It is a huge Peanut Island weekend, and there will likely be a lot of boats with less than sober drivers pulling up to the beach in that area to drop friends off who parked at Phil Foster Park. After a whole day of drinking they likely won't be paying attention for divers.