It is less about swing and more about clearence over your cross slide, combined with material weight and how you intend to support it.
You have said the diameter is 7", but how long and how heavy is the material you intend to machine? will it need supporting with a fixed steady and tailstock centre or is it short enough to be held securely by the chuck alone?
You will also need to know if you can bring your compound out enough to be able to use your cutting tools.
As an example, a mini lathe is sold as being a 7" x 16" so 7" swing, 16" between centres. HOWEVER, figuring the height of the cross slide into the equation, that reduces actual swing to 4-1/2", thus losing some of the "advertised" swing, which is usually measured over the bed, not the cross slide.
As I am unfamiliar with a Southbend, I can only suggest you measure from the centre of your spindle to the top of the cross slide, then double that measurement to get the "usable" swing over the cross slide. I would also suggest seeing just how far back you can get the compound slide and see if you, theoretically, have the space to achieve what you intend to do.
Sometimes, with a little ingenuity, large diameter stock can be turned with very minimal clearence and using "odd" methods.