Get battery health via Apple Configurator
Based on this article and others on JAMF Nation:
https://www.jamf.com/jamf-nation/feature-requests/6836/info-on-battery-quality

It doesn't appear possible to do this through Mobile Device Management (MDM) which is how you would need to do this if it were possible as you would need a server somewhere that the device could report back to.

As Apple Configurator only creates provisioning profile for managing device settings, but doesn't actually have a server side element I don't see how it would be possible to get this information back, so I would suggest the answer is no not with Apple Configurator, and also no not with the currently provided APIs for MDM.