When using the peashooters, the zombie always seems to destroy one plant, before walking towards the shooter. Also I've not seen the peashooter autonomously target a zombie, I've always manually targeted it, but perhaps I've not been patient enough. Seeing my garden getting scarfed down, doesn't breed patience!
One other thing to be aware off - if you fence off your whole garden, this won't keep the zombie out, as they can spawn inside your lot. So if you have a large gardening plot this can be troublesome.
I can see zombies being the new paparazzi. I can see control options to turn off vampires, werewolves, fairies and witches, but can't see one for zombies.