As a qualified "rain sound critic", to my ears the generated rainfall didn't sound convincingly natural. Real rain is somewhat less "white" (lets call it "gray"), with a steadier, if muffled "thud" as drops hit land.
Of course there are many variables, like wind speed, rate of rain accumulation, soil conditions, urban vs. rural location among others, that alter rain's sound qualities. Accounting for these factors would probably be quite difficult. Too bad the website didn't provide more info about the sound generation algorithms, I think HN readers would appreciate that.
As far as applications of generated sounds go, I think it's a very individual matter. In respect to tinnitus, a condition I've had for a long time, it's not a problem only when things are quiet.
In my case the internally generated high-pitched squeal is constant, loud enough to interfere with normal conversation. Adding external noise doesn't decrease or "mask" the tinnitus, just makes it harder to distinguish sounds in the environment.
One more thing, having known hundreds of adults with ADHD, mileage varies considerably re: benefit or decrement of background sounds on concentration. Offhand I don't know of studies documenting effects, but it would be an interesting study to conduct. My guess is most would do better in a quiet, but not too quiet environment. The issue is precisely what is "quiet" or "too quiet" for these individuals.