Reducing voltage for increased current through wire
I think you've confused several concepts here, but the short answer to the question I think you're asking is no, you can't increase the allowable current in a wire by reducing voltage.

The allowable current for a given size wire is determined by the how much temperature rise is acceptable in the wire and by how much voltage drop is acceptable between one end of the wire and the other.  The heating limit of the wire sets the allowable power loss per unit length.  Since wires have resistance, the power loss in the wire is equal to the current squared times the wire's resistance.  Heating limits are usually determined by applicable standards, for which various tables are generally available.  

The maximum allowable voltage drop depends on the application; you would have to know the characteristics of your load to be able to determine how much voltage drop is acceptable. 
 Because the resistance of a wire is a function of it's cross section and its length, shorter wires of a given gauge will have less resistance (and thus less voltage drop) than longer wires, so the length is a factor as well.

Where I think you may be getting confused is that if power is held constant, reducing the voltage requires increasing the current.  So for a constant power load like a switching converter, reducing the voltage will mean that the converter has to draw more current from the supply to maintain its output power.  In contrast, a resistive load like an incandescent light bulb will draw less current from a lower voltage supply.

To get more power through a given size wire, you generally need to increase the voltage.  This is why mains power distribution systems generally use very high voltages (hundreds of thousands of volts) for high power/long distance distribution links.  The voltage is stepped up for transmission, then stepped back down again close to the point of use.  As similar strategy can be done in a battery power distribution scheme as well, but the cost versus benefit for a small system may not make sense.