If you're on a smaller plane it's always a bit of a crapshoot. It's going to depend on how crowded the flight is but American Eagle seems apt to leave stuff behind for another flight if they don't have space, same with any airline flying smaller planes. (Have not been on AE to Bahamas but experienced this on other routes.)
When you're meeting a liveaboard, it's a decision you always have to make - fly in close to the departure and take a chance of a delay that means you or your luggage miss the boat, or play it safe and take an extra day. So, if I were going through say Miami on a summer day (often all screwed up by thunderstorms), on a smaller plane that is likely to be full and might not have room for all the checked luggage, with layovers that are kind of short, yeah I'd consider going the day before. If I was going someplace on a big jet in the spring and the schedule wasn't too tight, then I wouldn't worry.
There are cases where boats will wait some if they can, depending what's going on. And of course for a price you can usually find a way to get out to a boat that has left, but probably not something you want to do.