Yeah, you would significant time on some routes (e.g. NYC to Sydney or whatever), but in practice, the modulation time is probably going to kill you even if the neutrinos make it there faster. In the most extreme case (antipodal communication), the neutrinos take 43 ms to traverse the Earth and radio takes 67 ms to go around the Earth (ok, in practice a bit more since your fastest path would be via LEO satellites, and each hop adds a bit of latency, but it could be made small). But RF signals have MHz-GHz of bandwidth and huge SNR.

To take advantage of being 20 ms early, you'd need to be able to detect neutrinos at greater than 50 Hz from the other side of the world. For context, the planned 40 kton DUNE far detector a mere 1300 km from the world's most powerful neutrino beam at Fermilab, will have a neutrino rate from the beam of a few a day. So yes, highly impractical.