Disneyland has done this with food, and it's really really irritating. Here is an example of what it is like to get Blue Milk at Star Wars Land in Disneyland:
1) order it in the app and pay for it.
2) it tells you when to go there
3) wait for your phone to turn green, with a group of other people staring at their phone. A person is there to make sure people without green screens don't get in line.
4) you are now allowed to get into a line and wait.
5) you get to the front, and you repeat the order. Someone makes it for you.
I get the desire to replace cashier's with an app. But just let people place an order, give them a number, and let them know where they are in the line.