A "sickening sight" with a "list to the port" and "sails in rags" that requires constant pumping to stay afloat, to be precise -- with predictable results, namely getting sunk in one shot by an American merchant vessel. Were letters of marque really granted to vessels with such a low chance of success? Could any fisherman -- royalist or separatist -- really get their hands on one?
EDIT: Gah, "see serious naval action." At least it's an innocuous Freudian slip.
EDIT: I completely misread the question. See below.
Ah, that's a good one to sing at the pub.
There were no apparent rules in a Letter of Marque about condition of the ship, though in this one endorsed by John Hancock, you'll note the size of the ship is noted as thirty tons. Perhaps someone will chime in on exactly what size ship this would be, but it's not very large. More important to the Continental Congress was that the owner post a bond which would be forfeited in case of damages. And as can be seen in these instructions he'd pledge not to raid American ships, and not do piratical things like rape, torture, murder or ransom captives. Considering that quite wealthy people like Robert Morris and William Bingham were commissioning many privateers , going into partnerships with captains who wanted to become privateers, ( and doing quite well from them) the bond was not too big an obstacle for a willing captain. A greater danger than condition of the boat might have been British ire: they did not recognize the privateers as legitimate combatants and wouldn't parole them when they were captured, so thousands of captured American crewmen died in British prison hulks.