Best Buy authorized service for battery replacement

As mentioned, only the location you are going to can answer that but generally speaking, they tend to have batteries available since they advertise the ability to replace batteries same day. Also, usually if you schedule specifically for battery replacement they will have the battery on hand for your appointment date.

Since no one here works for Apple or most likely Best Buy, all we can tell you is to check with the Best Buy store to make sure they have the battery you need for your phone in stock. They are most definitely an Authorized Service Provider, but even if someone in another city had their battery replaced at a Best Buy store, that in no way would mean the battery you need is in stock at the store you'll be visiting.

No one but the staff at the actual store could answer that.

Call them to make an appointment.