I think it would be better to have the 8th gear be the one that doesn't work. If the limit screws are set correctly it won't even be possible to notice the missing 8th gear because the shifter won't be able to move past the 7th, as it will be constrained by the cable being tight. It will be just like having a 7-speed shifter.

If the extra gear is the first position on the shifter, it will be possible to shift into it, and nothing will happen except for the cable becoming slack and possibly snagging on something.