If the plane arrives on time, and you're the first one off and through customs/immigration, and your bags are the first ones to get into the terminal, then it's possible, barely, but I doubt it.
The trip from the airport to the water taxi terminal is 20 to 30 minutes depending on traffic. There are a couple more water taxi departures later in the day.
There is another water taxi company, but their schedule also has a 1:30 & 3:00 departure (same as Caye Caulker water taxi).
http://www.sanpedrowatertaxi.com/index.html