Yes camera batteries can be shipped through USPS as long as they are packaged properly.
I've shipped cameras and camera batteries together before and never had any problem doing so.
The USPS allows you to ship small batteries, laptop batteries, camera batteries, AA batteries, AAA batteries etc through the mail.
Batteries such as motorcycle batteries, car batteries and other larger batteries cannot be shipped through USPS.
But camera batteries and other small batteries can be shipped through the USPS.
Many people ship camera batteries and other small batteries through the USPS all the time without any issue.