Apple claims they do replace the batteries. I believe the ‘Used’ batteries are still tested through a diagnostic before they replace it, but I have never encountered anyone that has not had a brand new battery from a refurbished iPhone.
My nephew works for Apple, and confirmed that the shell and battery are both new in the refurbished units.
Just 2 weeks ago we bought my son a refurbished 8+ through his employee discount, as my son still wants his phone to run in landscape mode just like an iPad with 1920x1080p screen and touch ID, and it indeed looks and runs like a new iPhone.
If not for the lack of a photo of an 8+ on the box, I would not have known it was refurbished it was so clean, with new accessories, and the box still has all the other markings and bar codes that match the IMEI and SN of the phone. (with employee discount the 256GB 8+/AC+/tax/1-day shipping was $370 cheaper than a new Xr 256GB with AC+ and tax.)
We have enough reasons to believe the battery is new. The Settings > Battery tells him the battery is at 100% capacity. And battery life is excellent - my son took it off the charger at noon on Saturday, and at noon today, after 48 hours, the battery was still at 35% (he doesn't get all his mailed pushed to him, he stopped running apps in the background, and stopped using his Apple Watch so battery life is better on any phone he uses.)