No Zombies are soulless creatures of the living dead variety. They are mindless animal like beings who operate only on instinct. That instinct being to eat living human flesh, and blood. They’re human corpses brought back to life devoid of a spiritual connection to their souls. This is due to the zombie virus altering the DNA, and spirit frequency of the body to neutral. That means the body can not be possessed by the ghost of the original inhabitant, an angel, a demon, or any other entity. So the soul of the dead person residing in Heaven would not re-enter their body when the corpse is reanimated nor would it have any memory of being a zombie. The body in that case is just a pile of smelly rotting flesh walking about slowly with sharp teeth ready to perform cannibalistic acts.
Zombies may also be transformed from living humans who are bitten by them. Once they completely transform into a zombie they’re considered dead, and their soul goes to Heaven even as their body continues to operate beyond their control on automatic. However the deceased would have memory of the transition to zombiehood. It’s the closest anyone can come to having the experience of being a zombie. Those of you who must face family, and friends becoming zombies can rest assured they’re not really that person anymore. So please don’t hesitate to eradicate the walking corpses for the protection of yourself, and all those still alive.