Yeah, such a measurement is extraordinarily unlikely. Neutrinos are extremely hard to detect, but the thing is there are different temperatures of neutrinos, and their detectability scales extremely non-linearly with temperature. Even with extremely high energy/temperature neutrinos from supernovae or stellar fusion we still only detect the faintest fraction of the vast quantity that flows through the detectors. The CNB is at a temperature of only a few Kelvin, and is made of extremely low energy neutrinos that are effectively impossible for us to detect, let alone study with current technology.