Nope. The voltage is whatever comes out of the power supply. The driver has no control over that.It achieves its function by varying its own resistance so that the resistance of the driver + the resistance of the string of LEDs allows a target current to pass. It's therefore controlling resistance, the voltage.
1 single 4.2v (Fully Charged) lithium battery will supply max brightness (in the flashlight world they say "direct drive", most would say a short i guess lol)
The voltage out of the power supply has no relevance here.