Given a transformer with a dual primary winding (generally used to step down a series 220v or paralel 110v), can I instead hook up one winding to a 110v input and use the second as an isolated 110v output?

What kind of power restrictions or undesired behavior might this cause?

EDIT: This transformer, for example: http://mouser.com/ds/2/410/media-1067445.pdf

EDIT2: Added 24v to the image secondary coil for clarity