If one has to make an actual appointment to have the battery changed, I'm not sure why it would be necessary to wait much more than the time it takes to do the actual replacement. I mean, I can understand if one just walks into the store and asks for a replacement, the response could reasonably be something on the order of "OK, there are X phones in front of you, it'll be tomorrow at Y o'clock."
But if I make an appointment, I personally would expect the replacement to be done right then and there, i.e. the store has already told me what day and time the end of the line is and told me to come in at that time. I wouldn't expect to wait more than the time it takes to do a couple of replacements, depending on how many people are actually doing such. I mean, I wouldn't make a doctor's appointment and then sit in their waiting room for two days, I'd go in at the appointment time be seen right then. (Yes, my doctor is great at scheduling. I've never had to wait more than 20 minutes or so, so I'm spoiled.)