Yes, that seems to be the original approach, similar to a PLL design. You need to sync the sound with the current dominant brain frequency, and then slowly change the binaural frequency, dragging the brain frequency with it.

Whether this actually happens is open to research.

If it dragged dominant EEG frequencies, that would suggest that the effect either alters thalamic pacemaking or otherwise takes over. This audio beat frequency may exist as an analog somewhere locally as changes in average postsynaptic potentials in the auditory cortex, but it would be surprising if the effect grew to a larger sphere of influence. Healthy brains are pretty good at attenuating that kind of insidious network effect.