You couldn't make it the disgusting super saturated diabetes juice like they do in the south without heating it though. Mr 'Im not racist but....' is actually right about that.
Sweet tea usually has 2 cups (400 grams) of sugar per gallon (some "real southerners" use more.. a lot more)- so a 16 ounce glass (11 ounces of liquid, accounting for ice) will have (at least) 34.37 grams of sugar (about the same as a coke). A sugar packet has 2-4 grams of sugar. So, if you get the small ones, you'd need to sit there an open and pour about 17 packets of sugar.
They will dissolve. The saturation limit for sugar in 0℃ water is 180 grams per 100ml. There are 29.57ml per ounce, so 325.27ml in 11oz. 180gm * 3.2527= 585.486gm. So, you can dissolve 585.486 grams of sugar (or 292 sugar packets) in 11 ounces of 0℃ water.
You could do more if it were boiling- 490g of sugar can dissolve in 100ml of boiling water, so 490 * 3.2527 = 1593.823 grams or 796 sugar packets in 11 oz of water, but honestly, that seems excessive, even for the south.
In Arkansas, the standard is a cup and a half per gallon unless you're at a restaurant with a majority of black employees. Then it's two cups per gallon. I agree with the op on adding sugar to cold unsweetened tea. Fucking Yankee heathens.
Or, you know, don't add sugar at all. Iced tea doesn't need it.
When you stop guzzling that sort of syrupy sludge drinks start becoming refreshing. They quench your thirst instead of making you want to grab some pork rinds and a side of insulin.
Saturated at 100℃ is 490gms per 100mls or about 40 pounds per gallon. Most recipes call for 1 pound (2 cups) per gallon. A lot of people will double or triple that, but for it to be supersaturated at 0℃ you would still need about 15 pounds, so even taking it from boiling to iced, most people won't be supersaturating it.