From my experience No they will not stop, if they can find poop they will eat it, be happy she doesnt eat her own. We no longer have a cat because of this.
And as far as health concerns most farm animals, birds & ferrel cats carry coccidiosis & other diseases it will be very important to keep your dog
wormed , I use albon to control the coccidiosis. It is transferred thru the poo this article helped me
coccidiosis but use this for treatment/prevention if you choose to
Albon 5% You can also just periodically take a stool sample to your vet to be tested for around $10 to make sure there are no parasites, no office visited needed so no $30 office fee
. They all like the cat poo, I use to bring the litter box in the living room w/poo & then if they tried to get close scold them, thought it would help. I actually cut a little cat door so only the cat could get in, since before I would have to keep the door open for the cat-but a little dog can fit thru the cat door so...we no longer have a cat. I use to come home with cat poo & litter drug every where
I would be so pissed. Then the neighbors cats crapping all in the mulch, we replaced all the mulch w/pea gravel which they will still crap in but I spray it w/some bleach water to keep them away. So even after rehoming our poor cat, then more work & money because of the neighbors cats, then a chainlink fence to help keep them away from bunny & deer droppings $cha ching$cha ching$. All the research & vet visits $ trying to figure out a way to keep them healthy w/o going broke. So I ask ya, do I love my yorkie, well do I ...punk-lol Darn this Cursed Yorkie Love
Wish I had better news for ya. sounds like the auto litter box is a good idea, a gate maybe but some yorkies are climbers & then maybe a tie out in a designated area when she's outside to keep her away from the poo poo hot spots til you can figure something else out. Boy I'm windy tonight-sorry.