While there were considerable boycott efforts during the American Revolutionary war, even at that time there was a significant business in smuggled Dutch tea imports. After the war ended, tea drinking rebounded pretty well. There are, suffice to say, numerous references to it being a popular beverage throughout the late 18th century. Some particular die-hards promoted indigenous herbal teas as an alternative to imported tea, but this found little traction. So yeah, the status of tea in American culture was relatively unaffected by the war.

As for sweet tea, that's a slightly more complicated question. During the 19th century, iced tea drinks were popular among elites but they were usually punches or cocktails, spiked with alcohol. Also, they were usually made with green tea, rather than black tea, which wasn't particularly available in the Americas at this time. Some of this tea was, in fact, grown in the south. South Carolina maintained the United States's only tea plantations. Even so, at this time there was nothing particularly Southern about iced tea drinking as a practice. The first recipe for sweet iced tea as we would recognize it now comes Housekeeping in Old Virginia by Marion Cabell Tyree and dates to 1879. But just a few years later, a similar recipe is provided in a 1884 a cookbook from Boston, Mrs. Lincoln’s Boston Cook Book: What to Do and What Not to Do in Cooking, by D.A. Lincoln. There are also numerous references in newspapers from across the country attesting to the popularity of the drink, and none mention any particular regional bias that we'd be familiar with. Indeed, in 1868 the New Orleans Times implies that iced tea is a drink particularly enjoyed in the north.

In the early 20th century the drinking of iced tea became more widespread still, fueled by cheap black tea imports from India (and the unavailability of green tea during World War II) and the decreasing cost of producing ice. Ultimately it wasn't so much that the South uniquely adopted sweet tea as that they retained the practice while it started to fall out of fashion in the North. Even then, even identifying drinking it as a Southern cultural practice is relatively recent, with strong indications of it in media only coming in during the 80s and 90s. This accompanied a general trend in Southern food culture of viewing scattered and disparate local food traditions as being part of a larger Southern culinary tradition.