There was some discussion in the past from others who encountered problems over time that putting an LED headlight on these bikes tended to cause premature electrical system failures. Thinking was an LED takes less current, leading to the regulator needing to dissipate more current than it was designed for, as the draw of a standard bulb was designed as part of the electrical system. It will be interesting to see if you encounter an issue or not.
That doesn't sound right. All that would happen is that there would be less resistance on the engine. It's not like the engine is set to a specific RPM/power output at all times, so it'll just be that much easier to spin it (obviously very marginally so, this isn't something you could notice or even measure without really high quality equipment). The regulator won't factor into this, it'll just draw less AC current from the stator, and the stator will have less impedance with less electrical load. Couple of ways to think about this:
1. Imagine you disconnect the output from the rectifier completely. It's still got 12 V on it, but 0 current. Would it burn out? No, it's not like the voltage will go to infinity and it's definitely not shorting the output through some variable resistor to "burn" some kind of extra current. If this was the case, all your USB wall chargers without a phone plugged into them would blow up.
2. Imagine that you are on a bicycle with a stator and a regulator. You connect a very big load to the output of the regulator, something like a microwave oven. When the oven is on, the pedals will be harder to push because of the impedance in the stator. Soon as the microwave turns off, the pedals will be easier to push. You can actually try this if you have some basic electronics on hand.
Again, I cannot emphasize enough that the amount of additional resistance to the engine is tiny. We are talking about an engine that is rated for 16 hp = 11,931 Watts. A 12 V 2 A bulb is 24 Watts. Reducing that to a 5 W bulb will save you 19 Watts, or 0.16%. You can triple that for the inefficiencies in the system if you want, and still have less than 0.5% power gains. Losing 1 lb of weight would for comparison save you 0.19% of the power/weight ratio, so before I start a crazy trend of everyone thinking they are making their Rebels faster with this, you'd be better off losing 10 lb than swapping all the light bulbs.
Having said that, I replaced my headlight bulb with a $5 Chinese LED. If anyone wants I can link to my write-up about its brightness and how it all went. Basically though, super happy with it. It also allowed me to add fog lights for even more night time lighting. All my lights except what's in the clock are currently LED, and I'm super happy with it.