We can detect the CMB which, using the Stefan-Boltzmann law [s-b] and a CMB temperature of 2.725 K, is about 3.12e-6 Watts/square meter. But, the CMB is pervasive. The blackbody sphere you're asking about is very far away, and the amount of power you'd receive scales like the inverse square of the distance from the sphere to us here. So forget it, the CMB's blackbody energy flux on/near Earth is ENORMOUS compared to the star's.

[s-b] https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law