yes,
the MP will drive the lux harder.
actually, i use MP with one lithium ion cell at 3.6~4.2V to drive a 5W lux. Dunno the current to the lux but it is pretty bright.
if you use it to drive 1W lux, you may drive the lux at 800 mA or 1 amp
The MicroPuck draws about 460 mA @ 3V when driving a Q bin LED in my test setup. When I push the voltage up to 4.5/5 V the current consumed by the MicroPuck edges up to 600/700mA. Since the LED is intalled in a BBB McLux head with AA I don't have a way to measure the actual drive to it. I did not leave the voltage this high for any length of time.
If I get a spare Q bin maybe I'll test it to destruction with the MicroPuck. It'd be interesting to see which dies first.
The Specs for the MicroPuck say it can be driven at higher voltages than 3.0 V but not in the default configuration.
The MicroPuck is a ZLT boost converter. If you drive it with higher voltage than the Vf of your Luxeon, you goes into DD mode. If you have good enough heat sink, there is nothing wrong with this setup.