I'll bite - yes it certainly did contemplate privately owned weapons of this type. See Article 8 Section 11 of the Constituion which grants congresional power to "grant Letters of Marque and Reprisal". A letter of marque is used by privately owned warships, which even in the 1700's would have had devastating firepower. That settles the issue for me quite easily.
http://en2.wikipedia.org/wiki/Letter_of_marqueSo, do you suppose this gentleman had been issued a "Letter of Marque" by Congress?