No. For example, in a supernova, the neutrinos leave the star a few hours before the light does (since they don't get slowed down by all the mass in between). That's why for example we were able to detect SN 1987A's neutrinos before the light arrived. Similarly, the Supernova Early Warning System has been set up so that astronomers can point their telescopes in the right direction before any of the light gets to us (because we can detect and pinpoint a close supernova from the burst of neutrinos).