The driver is designed to draw constant power (volts*amps), so higher voltage cells will push LESS current, not more. I'd expect a draw of about 2.4A, runtime of about 45 minutes.
This is also a good application for the Kaidomain 2D LiIon pack. With 7.4V average, and 5Ah, it should be able to drive the LEDs for over two hours.
Both NiMH and LiIon have fairly "flat" discharge curves, and low internal resistance, so you can estimate runtime for both of them based of of the mAh capacity. With Alkaline cells, they have a high internal resistance, so "sag" severely under heavy loads. An alkaline that delivers 20Ah at 100mA current, might deliver <10% of that in a load like this. Alkalines aren't really suitable at all for the quad due to the high current draw.