Increasing the wire gauge decreases
resistance (because electrons have more area to flow through). And it's not just a matter of resistance anyway. The power that can be supplied on a given rail is limited (for example, 10A at 12V would be 120W). Adding a second circuit essentially means connecting a second source (so another 12V, 10A, and 120W source) to meet the power requirements.
This is why you should double check whatever PSU you use. Using a 4-to-6 pin connector won't matter if the rail its coming from can't source enough current.
EDIT: Coming from EVGA's site, this is what you need.
Minimum of a 450 Watt power supply.
(Minimum recommended power supply with +12 Volt current rating of 24 Amps.)
So if your 6-pin PCIe from your PSU can source 24 Amps, it will work. If it won't, then you'll need the 4-pin to source the additional current from a separate rail. If that 4-pin is on the same rail as the 6-pin, no dice.
On second thought, let's not go to TechReport. Tis a silly place.