As soon as you add a relay to your halogen headlight system, you will not only reduce the electrical load through the headlight switch, but also increase the voltage significantly at the headlight terminals which will result in more light on the road. Typically with the OEM long undersized wiring runs that go through the headlight switch and the dimmer switch, the headlight output (in Lumens) is reduced to about half.
Using a relay for the halogen headlights, the gain alone will be worth the effort. In general, American bulbs need 12.8 volt differential (measured at the headlight terminals with lights on) and European headlights need 13.2 volt at the same location for 100% of the bulb's rated illumination.
- John