You sure could!
The Zombie effect would just be a 'state' that would effect the player (either by default or added from an attack).
It would be:
Sp Parameter - Recovery Effect -100% (Now healing items/effects hurt the user)
Elemental Rate - Death -100% (now death magic/effects you have set up will heal the user for the value they would have damaged them)
So if I had a spell called "Inflict Wounds" that I want to heal undead or hurt living. I would set its damage type to 'Death', and anyone with the Zombie condition would be healed by it...and anyone else would be damaged by it. If you want the death effects to deal 0 damage instead of healing them:
Elemental Rate - Death 0% (instead)
You can then also give the Zombie status a few immunities to make it so that certain abilities can't affect them. I have a spell in my game that instantly could kill an ally, and it is 'death magic' so I would make them immune to that (even though it does no damage). So i would add :
State Resist - Death (what I named it...note : this is not state resist "Knockout" which is state 1, which is what happens when you get to 0 hp, this is resisting the state of the spells that instantly kill).
I hope that helps!