Could the Busemann's biplane concept be used in a turbofan engine?
No.

The Busemann biplane is a clever concept to have all shocks cancel each other, but unfortunately, the same canceling happens to all the lift. Therefore, a Busemann fan would not create any thrust.

The key of the idea is that shocks occur only between the two wings, the outer surfaces being aligned with the external flow so no shocks are created there. This means the concept would only be workable if every other gap functions as a Busemann biplane, the rest having straight and parallel walls.

In addition, the concept only works at one specific supersonic speed which depends on the geometry of the gap between the wings. On a fan you get a continuous increase in Mach number when moving from the spoke to the fairing. At Mach = 1 the chord of the wing would have to be zero for the concept to work over the whole span.