No. It’s just for communication purposes so anyone can help out with the customer

It does mark out on mobile if you mark something out using item availability on the POS. There used to be two ways to mark stuff out, one that was only for mobile and one that was for in store. But they changed it to be just the one system a while back.

If a store is out of something sometimes it tells me on the mobile menu, it'll be crossed out and say it's unavailable or out of season but I've also had where I can add a drink to the cart but it won't allow me to check out saying the store I've chosen is out of oat milk. Only after this notification is there a red note in the cart saying no oatmilk at this store. Have also ordered pastry and when I go to pick it up, they inform me they are out and take me to the register to refund

Not sure if that's what you're asking but thought I'd share my experience when ordering on mobile. 💕