Yes, it would be possible to make this trip on a Prindle 16 - but it will be relatively tough and 3 days would be more realistic. Do you have much experience launching through surf and what is the longest time you have sailed the boat for?
I'd recommend launching from the gulf side beach at Port Aransas to shave off a little distance (rather than launching from Mustang Island State Park). The first day will be the toughest - it is 100 miles to the beach at Matagorda jetty - and no where habitable to land along Matagorda Island (check out the charts or google earth). You could just chuck a couple of light weight sleeping bags and a little food and water in a drybag and camp rough on the beach on the tip of Matagorda Island, just before the Port O'Connor jetties.
The second day you could sail as far as Sargent or if the wind is good you could carryone to Surfside. From surfside it would be a relativly short day to East Beach, Galveston.
You would be sailing 2/3 of the Great Texas Catamaran Race. This race has two 100 mile legs back to back on the first two days. The first is from South Padre Island to Mustang Island (Corpus Christi). Along that stretch you could be picked up by a 4WD vehicle if you broke down (with a long drive on the beach, and padre island is split at Port Mansfield cut). The second day is from Mustang Island to Matagorda. Day 3 is from Matagorda to surfside (70 miles). Day 4 is from Surfside to East Beach, Galveston - approx 45 miles.
The Great Texas is sailed on F18 and Inter20s. The 100 mile legs took 8.5-10 hours last year - that is high performance spinnaker boats with experienced crews, and no camping supplied or other additional weigh on the boat. In some years the 100 miles has taken just over 6 hours.
I'm not saying don't make the trip - another person on this board did something similar on a Nacra 5.2 - just expect it to be an epic, and make sure you are comfortable in surf and don't expect an easy rescue if you break down on Matagorda Island.
Oh, and look out for the breakers on the north tip of Matagorda Island and the sand bars in San Luis pass. Both should be visible on Google earth.
Chris Green.