Absolute Thumbnail Column

Yes and No. This support all of the post type that supports post thumbnail feature.

This plugin does it’s things only in admin dashboard, and has nothing to do with themes.

We already implemented support WooCommerce’s product list table’s image column too.

No. The remove button on the thumbnail column only remove the post’s thumbnail (meta),
and doesn’t deletes the actual image from media library.
However you can delete the image from the media popup as usual.

Please check the Screen Options located on the top right corner on the screen and make sure Thumbnail checkbox is checked.
If not please click the checkbox and this apply to apply the changes.

Please make sure your post type is registered with init or any earlier hook with normal or higher (before 10) priority.
If the priority is too low (Eg. 9999) this plugin might not able to detect it.
You can also use the following 2 filters to add support for your post-type absp_post_type_supports_thumbnail && absp_current_post_type_supports_thumbnail.
It’s require that you use both of these to make your post-type get recognized by the plugin.

E.g.
add_filter( ‘absp_post_type_supports_thumbnail’, ‘add_your_post_type_thumbnail_column_support’, 10, 2 );
add_filter( ‘absp_current_post_type_supports_thumbnail’, ‘add_your_post_type_thumbnail_column_support’, 10, 2 );

function add_your_post_type_thumbnail_column_support( $supports, $post_type ) {
    if ( 'your-post-type' === $post_type ) {
        return true;
    }

    return $supports;
}