According to Osho, yes—realization can dawn even in the animal state; awakening is a function of consciousness, not species. “Previous birth” means any past life, not necessarily the immediately preceding one, so ripeness can mature across many incarnations. When the inner readiness peaks, the breakthrough happens—whether in human or animal form.
Any being, even an animal, can wake up spiritually when they’re ready; it isn’t limited to humans or to the last life.