Chunk loading has little to do with mobs despawning.
At over 32m from the player, mobs have a chance to despawn at random. You could probably get away with being in this area for a short time, but eventually the zombie villager will despawn.
At over 128m from the player, mobs will despawn instantly. Neither of these values are affected by render distance.
Passive mobs and named mobs are excluded from this limit. If you want to keep the zombie villager, one possible method to do so would be to name it with a nametag. Although, in all honesty, zombie villagers are common and not worth the hassle; just find a new one when you have the right supplies.
The other answer is provably wrong:
Create a new superflat world, spawn a spider at your spawn, and then teleport (/tp ~1000 ~ ~) far away from it. When you teleport back (/tp ~-1000 ~ ~) the spider will have instantly gone, even though those chunks stayed loaded.
Also try spawning a spider outside of the spawn chunks, then set your render distance to 2. When you see the chunk with the spider unload, it should despawn, right? If you go back into the chunks, so long as you didn't go too far away, it'll still be there.