When Comet Cache is installed in a WordPress Multisite Environment, it must be Network Activated. This results in Comet Cache being enabled on all sites in the Multisite Network. If you want to restrict Comet Cache so that it's only enabled on the Primary Blog, you can use an MU-Plugin.

Create the following file and directory: wp-content/mu-plugins/zc-restrict-to-primary-blog.php

<?php
add_action('init', function()
{
    if(!is_multisite())
        return; // Not applicable.

    if(!defined('DOMAIN_CURRENT_SITE'))
        return; // Not possible.

    if(!defined('PATH_CURRENT_SITE'))
        return; // Not possible.

    if(strcasecmp($GLOBALS['current_blog']->domain, DOMAIN_CURRENT_SITE) !== 0)
        define('COMET_CACHE_ALLOWED', FALSE);

    else if(strcasecmp($GLOBALS['current_blog']->path, PATH_CURRENT_SITE) !== 0)
        define('COMET_CACHE_ALLOWED', FALSE);
});

How do I know Comet Cache has been disabled on the Child Blogs?

If you visit a Child Blog (while logged out of WordPress, as Logged-In User Caching is disabled by default) and "View Source" on one of the Child Blog pages, you should see a message like this at the bottom:

2015-03-28_13-05-41

This indicates that the MU-Plugin is working and limiting Comet Cache to the Primary Blog.

How do I hide the Comet Cache HTML Notes?

You can disable the HTML Notes in WordPress Dashboard Comet Cache Plugin Options Enable/Disable.