I was told that Apple Care only covers the watch, not the band.
Apple hardware coverage
AppleCare+ provides repair or replacement coverage, both parts and labor, from Apple‑authorized technicians. Service coverage includes the following:
Your Apple Watch
Battery1
For Apple Watch and Apple Watch Sport, included magnetic charging cable and power adapter. For Apple Watch Edition, included magnetic charging cable, power adapter, charging case, and USB cable.
Coverage for up to two incidents of accidental damage from handling of your Apple Watch, each subject to a service fee ($69 for Apple Watch Sport, $79 for Apple Watch, $1000 for Apple Watch Edition) plus applicable tax.