People talking about how the "government would return him in a flash" need to keep in mind that this is 1815, there are no real border controls and the U.S. federal government is weak. Also, most Americans in 1815 lived in the countryside and probably had very limited access to news from Europe; most probably would have no idea what Napoleon looked like and probably only a vague idea about the wars that had gone on. Even if the U.S. government wanted him apprehended, it would likely be dependent on an individual state government to use its militia to hunt him down, and that state might balk. (Would Louisiana want to turn him over to the British?) He could well escape detection (due to either incompetence or indifference by the state government) for quite awhile.