I don't think it will work. The module is a step-down converter, not a step-up. Of course you can always try just connecting 3 volts across the module to see if it lights. That should not damage it, since it's just like running on 4 almost-dead batteries. But who knows.
It would be great if they made a 2aa version of that module. As it is, they make a nice little 2aaa eLED light, but of course it's just a 5mm led.