Late last year there were major snow storms from the rockies to New England. Air traffic came to a halt, first at Denver. Remember those 200+ passengers stranded for two+ days sitting on the floor of the airport? I can unfortunately tell you for cerain that many on that floor were trying to get to their ship. Some on those cancelled flights had purchased cruiseline air, some had booked air on their own. Same thing a week or so later at JFK. Unfortunately, some people in Houston, Atlanta, Cincinnati and airports all over the country were waiting for those grounded flights to get where they were going. Didn't matter who they booked the air through, they missed the ships. The cruiseline didn't fly any of these people to Grand Cayman for the last 5 days of their cruise when flights resumed and neither did the airlines. Do ships occasionally delay departure for delayed flights? Yes, they on very rare occasions will hold a ship. Do they have to do so or guarantee to get you to the ship if not? Absolutely not.
Your only protection is not who you book your air through. It's in making a very small investment in travel insurance. Usually at or under .10 cents on the dollar of the cost of your cruise. That way, if you have good coverage, available through many sources you have coverage for trip interuption (that's what they call these type of outside expenses). You also have trip cancellation coverage, medical, dental, baggage loss & medical transportation (helecopter evac, private chartered fligh home for recovery, etc.).
Moral of the story, don't count on the cruiseline or airline to be benevolent, they're not. Protect yourself! Fly in a day early? Yes, if you can. But be aware things can happen that even flying in early wouldn't protect against. Get a good travel insurance policy and pray you waste the money when you do.