The machine should show the same absolute Z position regardless of the offset (i.e. Z-1.0).
The 'Distance To Go' will be more since the machine thinks your tool is now shorter by 0.200".
If the absolute position shows Z-1.200 then something is wrong.
There is a parameter that says something like 'Position Display Includes/Does Not Include Tool Offset Amount'
You want it set so the position does not include the tool offset amount. That way the absolute position display will always read the same as your programmed positions.