Not sure exactly how it works from port to port or cruise line to cruise line, especially in light of recent security issues...But, I do know that when we sailed the Millie out of Venice last year, not only could you board and then leave the ship all day in Venice, Celebrity actually somewhat encouraged it, providing a continuous shuttle to Piazza San Marco...Of course, this may vary line to line and port to port...I'm sure they don't want any interference with the normal boarding process and with security...
It will be interesting to hear from folks who have sailed out of San Juan recently...
FWIW, we don't plan on getting off the ship in San Juan once we've boarded...we're flying in a day early and plan on wandering Old San Juan, eating local, etc. the night before...Once we get on the ship, we're going to relax and get ready for Casa de Campo...
Which ship/sailing are you on?