The study had people wear electrodes to determine/drive the noise oscillation frequency. The noise oscillator was being controlled by the sleeping human (they used a PLL, which to me implies a bit of "catching up" lag if the human changed frequencies).

However, who's to say that the human has to be in control? You could replicate the study, but have the computer determine the oscillation frequency (or maybe just keep it fixed) and maybe find similar results.

The biggest technical challenge for a DIYer would be "comfortable enough to sleep in" electrodes.

Yes, it should work but make sure the app is genuine. Really though, even a table fan works.