There is a CSX line in place between BHM and ATL, via Irondale, Ragland and Ohattchee. This line sees a couple of freights a day,It would be the shortest re-route by mileage, but probably not travel time.
The route you are talking about can not be used, as it no longer goes through. The line is the former Seaboard Airline Railroad main between Birmingham and Atlanta. Only the Birmingham to Wellington AL portion remains. East of that point it has been abandoned. At this point it meets the remnant of the formere L&N's Alabama Mineral line that ran from Calera AL to Gadsden AL. This line, which went through Anniston, has been abandoned south of Wellington.