It depends on the Apple store. Most now are able to replace the battery and hand you back your same device within 30 minutes. They did that to my wife's phone. We paid our money and left, but had to go back for a replacement phone immediately cause the battery replacement didn't go well and the phone was going nuts.
Call your store and ask if they replace batteries in house. But back up your phone before taking it anywhere. If you do an encrypted backup, the new phone will be set up like your old one with passwords still remembered after you restore.
Thanks. We don't have Apple Stores here, just apple-certified service providers.