I'm in St. Martin right now, although I'm on the French side in Grand Case.

The answer to your question, as so often in the Caribbean, is "it depends". If you anchor on the outside or inside of Simpson Baie you need to clear out of the French side first (Oyster Pond, Marigot, Anse Marcel) and then clear into the Dutch side. But the customs inspection rarely checks boats outside in the anchorage and tends to concentrate on the private boats rather than the charter boats. The Dutch have a nice system in that they charge you for a week at a time, so one night is just as expensive as are 7. The bridge fee isn't too bad and if you have people aboard and want to party then going inside and anchoring is preferable to being outside. Just remember that the Dutch require an adequately bright light at night, anchor, and lifevests aboard the dinghy - they won't stop you unless your light isn't acceptable and a flashlight actively swung around is considered sufficient.

Overnighting is different from dropping the hook during the day, and I would suggest you contact your charter company as they might have special regulations - i.e. Sunsail boats from Oyster Pond might be considered cleared in on both sides.