I would think - but could not put my hands on any evidence to back this assertion up - that such neutrinos would be unavoidably thermally coupled to the rest of the universe prior to 1 second [before this, the neutrinos are sufficiently coupled to electrons and positrons through weak interactions that they follow their temperature]. So, even though cooled massively by the inflationary expansion, they would be reheated, become part of the thermal equluibrium mixture in the early universe and become indistinguishable from the "conventional" neutrino background.
The numbers of decoupled neutrinos deduced (from the properties of the weak interaction) in this background are too few to explain the dark matter. They are also too "hot" at the epoch of radiation/matter decoupling to explain the rapid formation of structure.