You have to assume that other species would be unwilling to trade with you. Essentially treating you as a devouring horde. Though I'm not certain.WAIT...
Biggest roadblock to launching this.
What happens when a single Zombie immigrates into a non-Zombie empire? Or when a non-zombie conquers a zombie world?
It would end up converting the whole empire, right?
I mean it wouldn't "just" (if successful) steamroll the galaxy through genocidal conquest. It would assimilate the whole galaxy even if the Zombies were fanatic pacifists, right?
Do the Zombie Worlds automatically switch ownership, or is it just that basically all species eventually gain the Undead trait?
Honestly there's a lot of detail that would need to be ironed out and I can't see Paradox doing it just cause I ask nicely lol. Still I think there's something to it and the species and ship packs would be the cats pyjamas.
Think Firefly Reavers