It was probably known to Thomas Jefferson at least, by 1803.

Several of these air rifles were carried by the Lewis and Clark expedition which Jefferson commissioned and sponsored, so he might well have known about the gun.

The expedition gave demonstrations of these rifles almost every time they encountered a group of Indians. The impressive feature of the gun was the ability to shoot circa 30 shots before needing to be re-loaded (and have the compressed air reservoir pumped up - which took a while).

The objective was to demonstrate the massive firepower available to the expedition and thus deter any temptation towards hostile acts or theft.

Generally the expedition did not encounter hostility from the Indian groups met along the way. Whether the air rifle demonstrations contributed to this I don't know.

http://home.nra.org/history/video/lewis-and-clark-girandoni-air-rifle