Having worked in the field for years, I am pretty sure that listening to some sound at some frequency might induce that rhythm in the appropriate part of the brain (I have worked on SSVEP which is the same thing for visual stimuli, and is easily detectable, there is also some evidence that it could work for sensory motor stimuli).
However, inducing some frequency somewhere in the brain is pretty useless. Beta activity has been known for some time as the “activity” indicator. But this is simply because that is the working frequency of the brain. Active means just that, is it good is it bad? That depends.
One thing that strikes me in the field is how sure people are that anything “induced” in the brain will be positive. If the binaural beats thing really worked, then you would have as much chance to create depression as a sense of calmness.
And yet, eugenics was kind of heavily touted by scientists precisely because of an inability to accept as valid the personal experiences of the populations it targeted.