By chance, I found the following note in the Gentleman's Magazine and London Chronicle April 1765
so, they did try it.
The French neutrals lately settled in the western parts of the province of South Carolina have already begun to apply themselves to the breeding of silk worms, in which they have made some progress; and for their greater encouragement the governor has promised 500 dollars premium to the first who shall produce 10lb weight of raw silk, the produce of Carolina.
so, they did try it.