Not directly but it does give some clues that it is likey 1.2A-3A current driver with 2x 16340.. 2.4A is the max I like to draw from two 16340 personally and they don't last long at that current either.
Let's do some math. 30W output from a good diode laser means at least 100-120 watts of input power. At 7.2 volts, 100 watts would be a little under 14 amps.
So with the specified batteries the laser would have a maximum run time (assuming 2 Ah cells) of under 10 minutes and would get too hot to hold well before that.
No, a laser doesn't care what it gets it's input power from. But from the above it should be clear that the claims made by WL aren't very realistic.
If you want a 30 watt hand held your choices are an IR diode bar with really lousy beam specs and short run times, combining beams from multiple diodes, or a CO2 laser. All of the above will eat lots and lots of power. Lipo batteries would give you the needed power but the run time would be very short for any of those options.
Crows can see 460nm very well I found out one day, some were tearing at a garbage bag in my back yard and I just flashed the beam a few feet over the can and they flew away scared and never came back. Wouldn't want to hit them with it though. They must have good vision to that wavelength, more than I do anyway to scare them so much in the daytime.
Birds can see UV too. I read that hawks use this to hunt mice and they see the urine trail to find them. so 405 would look like maybe 638 per mw or maybe brighter. No wonder 445 would scare them off since It still has a violet tint to it unlike 473.
Slightly more off topic, In the case of dogs, I wonder if certain breeds can see some colors better than others? My brother uses one of those cheap red lasers in his back yard at night sometimes for his dog to chase, she loves it, loses her mind over chasing it, its quite funny. And dont worry, its a less than 1mw laser, and he never shines it at her eyes or anything. She is a Retriever/brit spaniel mix.
But then my girlfriend has a miniature schnauzer, and I tried shining cheap red and green lasers near him, and he doesn't react at all, like he doesn't see them.