It does. The headlight relay mod is more for US markets where they don't have the option to turn the lights off as standard.
The idea is to isolate the lights when the starter button is pressed. Its a way of trying to wring the last bit of juice out for starting.
IMHO its wishful thinking in some ways. Compared to the current draw from the starter the lights put a relatively insignificant load on the whole process.
You are talking about 1 or 2 amps and a half a volt drop versus a couple of hundred amps for the starter. Unless your battery is weak in the first place or there's some other deficiency in the wiring its not going to make a vast difference. But, in some cases, every little helps.
Paradoxically, for those of us using Lithium batteries the advice when the weather is cold is actually to make sure the lights are on for about 30s before starting. It raises the internal temperature of the cells which don't function at their best below about 5C. Turning the lights on brings the cells to life.