Is it possible to determine when user is at “Media > Add New” vs “Post > Add an Image”

I answered this for you in the comments of your previous question.

…you can use the filter that @Backie
suggested above
(intermediate_image_sizes_advanced),
and in the hooked function check for a
field in the post collection named
_wp_http_referer. It tells you where the upload request came from.

If _wp_http_referer contains
“media-new.php”, you can return an
empty array (which will temporarily
stop thumbnail generation, but won’t
actually change any thumbnail
settings). Otherwise, return the
$sizes array untouched.

Try:

function wpsx_7756_no_thumbnails($arr_sizes){

    if(stristr($_POST['_wp_http_referer'], 'media-new.php')) {
        return array();
    }

    return $arr_sizes;

}

add_filter('intermediate_image_sizes_advanced','wpsx_7756_no_thumbnails');

Let me know if this works.

Keep in mind that adding the filter while you’re on the upload form won’t do what you want–the form posts to a separate page that handles the upload, and it won’t respect your filter.