Glad you asked, Charley.

Acc. to the Gentleman's Magazine of 1839, it was Wallack's brother Henry who was in training as a midshipman around 1808. The teenaged James ran off to join him and wound up sailing briefly and unofficially on the French coast with his cousin George Allen Field, who happened to be commander of the gun brig "Desperate" (great story, eh wot?). Wallack's parents induced him to return to the stage by promising him the role of Hamlet.

Wallack had a long and distinguished acting and managing career after that.

So it looks as though he may have picked up his "chant" of "Sally Brown" at sea, or at least in port, without ever "serving" in any official capacity. While it could have been as early as 1808, there's really no telling. He could have learned it at second hand much later.