Well it is quite possible, when using a multisite you have a few extra tables in your database.
One of them is one that is called wp_site which has inside it a list of all your blogs.
It looks something like
site_id | blog_id | some other vars ...
1 1 ...
1 2 ...
1 3 ...
You would have to fetch all of these,
and then you could fetch all other posts comments using the $wpdb->get_results more or less like so,
foreach ($blogs as $blog) {
$blog_comments = $wpdb->get_results("SELECT c.*, p.* FROM wp_{$blog->blog_id}_comments AS c INNER JOIN wp_{$blog->blog_id}_posts AS p ON c.comment_post_ID = p.ID ORDER BY comment_date DESC LIMIT 0,10"); // Get the latest 10 comments from each blog and it's related post
}
Afterwards you would need to check for the posts category and post it on the front side accordingly.
If you need more help, comment here, I’ll try to supply more data.