Sure, you could write a program that periodically checks the battery rate (you'd have to poll since there's no ACPI notification like with a "device battery") and sends an email to the admin or something. However that's a tool that doesn't "exist" (as in, there isn't notable program that does so) which possibly hints that this isn't something system admins often do.
The above also requires there to be an interface available from userland, not only in the management firmware or BIOS/UEFI. That exists for HP, but I'm not sure all other OEMs do so.