I think it's quite possible, but it would take a different (but very similar) plugin. It would be connected to the OnUserAddToGroup System Event, but I'm not sure it would be reliable. It depends on whether MODX invokes that event when adding a user to a group. It definitely would not work when users are added to a group in code without calling the add processor.
Here's a way to check (untested):
Create a plugin with this code, connected to OnUserAddToGroup and OnUserGroupFormRemove:
$event = $modx->event->name;
$userName = $user->get('username');
$groupName = $usergroup->get('name');
switch($event) {
case 'OnUserAddToGroup':
$modx->log(modX::LOG_LEVEL_ERROR, 'User: ' . $userName . ' added to ' . $groupName);
break;
case 'OnUserGroupFormRemove':
$modx->log(modX::LOG_LEVEL_ERROR, 'User: ' . $userName . ' removed from ' . $groupName);
break;
}
Add and remove a few users from groups using the various methods in the Manager and see if you get a message in the error log.
If it works, the plugin could be modified to send the email in each case.