Check the calendar for the days they are open. They have a few closed days the first week of September.
The rest of September and October is Harvest Festival.
https://hfe.widen.net/s/hm2pjhbzhb/24dw_opcal_festivals
Everything runs every operating day, whether permitting, from March to Jan.
https://www.dollywood.com/themepark/Rides/Ride-Temperature-Guideline
Of course rides can have down time, and getting parts can take days/weeks.
And water rides, like Daredevil Falls and Smoky Mountain River Rampage, and are closed when it's too cold, but not an issue in September.