what happens when?

[creedtown182]

If I were to place the tailstock live center in a center hole that isn't concentric with the section of the shaft that I am chucked on, the chuck will now be fighting against the live center. This as I know can do one of two things, either make the live center "runout", or bend the shaft. If it bends the shaft, will the shaft still come out straight after being turned? Will the section of the shaft that is turned now be "out of parallel" with the section that is in the chuck?

[Spook]

If I'm reading what you wrote ,correctly, the answer to both questions is yes.