When I boarded MV Sun Princess in Costa Rica last month, many of the people coming from the West Coast who arranged their air travel through Princess did leave home on "red eye" flights. I don't recall very many people on prior cruises arriving in either Florida or Puerto Rico on "red eye" flights, but it depends to a large degree on which flights are available to get you to the ship in time.
If there are a lot of passengers from one area who are taking the same cruise, Princess may arrange a charter flight to accommodate those passengers. In such instances, the timing of the flight is controlled largely by the availability of the aircraft and flight crew.
Since Princess has to provide overnight accommodations at no additional charge if they arrange a flight on the day before embarkation day, it's a pretty safe bet that the cruise line will do anything it can to prevent such an occurrence.
BTW, the practical alternatives from, say, Los Angeles (LAX) to Fort Lauderdale (FLL) are:
>> a "red eye" flight to the airline's hub, connecting with an early morning flight to Fort Lauderdale (which will give you two or three hours to kill at the airport prior to transfer for embarkation) or
>> an early morning departure, connecting through a hub and arriving in Fort Lauderdale in the late afternoon or early evening.
The serious drawback to the latter is that there's little chance for recovery if your flights get snagged, though the ship may wait for you if you booked your flights through the cruise line.