Yes you can. In St Lucia you are allowed 24 hours to actually depart on a charter boat, 72 hours on a private boat. Noonsite ( link Noonsite ) is a good place to get the latest regulations.

Of course, in most places, you can safely say... Yes we cleared out yesterday intending to go straight to ( wherever) but had problems when we raised the sails so had to anchor here to fix the problem. Will nearly always get away with that although if the C&I people questioning you are corrupt (BVI for instance) they may try to 'fine' you a bit of cash.