Adding commas between post titles on an archive page?

If you ultimately want the last post, regardless of pages, then you need to use found_posts.

This could change depending on how you sort but I didn’t see any modifications to that in your code.

So to just modify the content of your code above you would do this:

<?php
    if ( have_posts() ) {
        $count = $GLOBALS['wp_query']->post_count;
        $total = $GLOBALS['wp_query']->found_posts;
        while ( have_posts() ) {
            the_post();
            echo '<a href="'. get_the_permalink(). '">'. get_the_title(). '</a>';
            if ($count != $total) {
                echo ', ';
            }
        }
    }

    wp_reset_postdata();

?>

Another way to do this could be to add the lines to an array and then implode it:

<?php
    if ( have_posts() ) {
        $myPosts = array();
        while ( have_posts() ) {
            the_post();
            $myPosts[] = '<a href="'. get_the_permalink() .'">'. get_the_title() .'</a>';
        }
        echo implode(', ', $myPosts)
    }

    wp_reset_postdata();

?>

Notice I changed the_title to get_the_title and the_permalink() to get_the_permalink() so we could echo instead of just displaying the them. I also changed your concatenators from a , to ..