It wouldn't stop the voltage drop, unless part of the original wiring had a resistance short somewhere and was using up power - but you'd probably notice that already from the burning smell
That kind of voltage drop normally indicates you don't have enough alternator output. Check the belt tension and check the connections to the alternator. If you have a voltmeter check the real voltage drop with and without the engine running. You may find the dash volt meter is only "Alfa accurate".