The exact terms and conditions will depend on the bus company's contract of carriage. Normally this would be the same as with most airlines: they agree to transport you between city A and city B and the details including routing of the service are not guaranteed. If you try hidden city ticketing it'd be at your own risk.
In practice you might be able to get away with hidden city ticketing as described in your example of Gadsden to Atlanta. Generally I'd expect using hidden city ticketing with buses would be more likely to work out than with flights - operational issues are less likely to reroute you far away from your route than with an airline network.
Other cases might be a bit riskier: Greyhound often adds extra "sections" = extra vehicles to a departure when there is high demand, on some routes and schedules these are used daily. Say you buy a ticket from Minneapolis to Chicago intending to get off at the stop in Milwaukee. The schedule running from Minneapolis to Chicago via Milwaukee might be run by two buses, it's possible Greyhound would run one bus express bypassing the stop in Milwaukee and not have enough space for you in the original bus making all the stops.
See my answer regarding skipping an previous or subsequent leg on Greyhound.