does apple care for macbook pro give you one free battery replacement

The battery would be replaced only if it retains less than 80% of original capacity. See the footnote below from AppleCare Products - Mac - Apple

Service coverage is available only for Mac and its original included accessories for protection against (i) defects in materials or workmanship, (ii) batteries that retain less than 80 percent of their original capacity, and (iii) up to two incidents of accidental damage from handling of your Mac, each incident being subject to a service fee of $99 for screen damage or external enclosure damage, or $299 for other damage, plus applicable tax. If your Mac has catastrophic damage from an accident or is inoperable

Within first year the battery may be replaced under initial courtesy

warranty; by an Apple authorized service or Apple store, etc. An

AppleCare+ plan may offer additional time for more covered items.

Conditions apply and charges too.

Good luck!🌻🐝