The OPERA experiment (of false FTL neutrino discovery fame) did create and detect neutrino pulses as part of their experimental setup. It's possible as far as

The OPERA experiment (of false FTL neutrino discovery fame) did create and detect neutrino pulses as part of their experimental setup. It's possible as far as the physics go but also impractical given the particle accelerator and detectors needed. And the post-processing the scientists had to do to tease out the timing information also would negate any latency advantage.