Ok... picture turning a crankshaft journal... the end in the chuck may be offset several inches, but the journal that is being turned would end up round.
Same concept... if your runout is caused by the chuck not holding the work pefectly concentric with the axis of rotation. What you machine will be concentric... and round, barring all other negative factors.
However, if the part is removed from the chuck, turned, then reinstalled, your machined diameter will now show some runout... theoretically, if it is turned 180 degrees, it should show two times the runout of the chuck.
-Bear