No. You specifically order "sweet" or "unsweet" tea in the South (or "half and half" if you want sweet but not cloying). Anywhere else, I would expect that sweet tea would be unavailable.

Note: this does not apply to bottled/canned teas, which are usually close to "half and half" in sweetness.

Most restaurants here serve soft drinks from a fountain rather than individual cans/bottles, so refills are free. If a restaurant uses individual containers for service, you will have to pay for refills. However, iced tea has free refills everywhere I've ever seen.