Actually, you shouldn't get any sound out at all, let alone a weak volume in the center of rotation.
Remember, electricity always seeks the easiest path of travel to complete a circuit., So let's analyze the signal flow with the wiper at the halfway point.
The incoming signal sees a resistance to ground over the first half of the total resistance, right? And there's an additional resistance between the wiper and the output, right? And if it's much easier for the electrons to get to ground via the wiper (and thus completing the circuit), then why would any of them attempt to get through the additional resistance and out to the amp?
Answer: They won't. Not at any point of the wiper's travel - the ratio of the resistance portions will change, but the net effect is, the grounded wiper will always be the easier path for the electrons to follow.
Moral of the story: This "mod" will end in tears.
</electronics lesson for today>
Rule #1: All Lives Are Final. Make sure that the life you have just been issued is appropriate for your needs, before departing the womb.
Rule #2: In case you don't like the life you have, see Rule #1.