I have been in Grenada since July and have not seen any transient boats anchor in the lagoon, and I believe there are just a few private mooring, probably "grandfathered" from the time before the marina was there. You would most likely need to anchor outside the lagoon and dinghy in to the marina to clear customs. Friends who have anchored there recently have told me the holding can be less than ideal, so take your time finding a sandy spot :-)
If you do end up stopping in Carriacou, clearance now takes place in Tyrrell Bay, rather than Hillsborough.