Possibly. In Halo 4, Cortana proposed that they could recompile her neuronet by replicating the same conditions as her old one, perhaps with another partial cloning of Halsey's brain. However, we now know that it wouldn't have been possible because Dr. Halsey was under ONI custody when chief and cortana returned to Earth and they wouldn't be able to contact her before cortana went rampant, so her death was truly inevitable.