Well, it all depends on amperage. I don't remember the math to calculate required input amperage (i.e. it would take twice as many amps at an input voltage of 12v as opposed to 24v) But you could give it a try just make sure you can unplug it quickly just in case

But as an example if the converter required 1.5a at 12v to give you the 6v conversion it would only require 750ma at 24v

So if you find the amperage difference (1500ma - 750ma = 750ma) and divide it by the voltage difference (24v - 12v = 12v) then divide the amperage difference by the voltage difference ( 750ma / 12v = 62.50ma)

Next to calculate the amperage based on a given voltage multiply the amperage interval by the difference of the given voltage and lowest voltage ( (15v - 12v)*62.50) = 187.5ma ) and then subtract the amperage we just got from the amperage at 12v (1500ma - 187.50ma = 1312.50ma )

So when the converter is given a 15v input it would require approx 1.3a. Now if said 6v device is not running at a full 2a it SHOULD be fine.