customiser settings for checkbox (displaying content)

Looks like you are missing some things from the settings array, namely type need to be theme_mod here and capability should be set too. You can try:

$wp_customize->add_setting( 'woocommerce_productdisplay' , array(
'type'        => 'theme_mod',
'capability'  => 'edit_theme_options',
'default'     => '1',
'transport'   => 'refresh',
'sanitize_callback' => '',
) );

Also note default for a checkbox should be ‘1’ for ticked. Then you would use slightly different code for the output also with this in mind:

<style>
#woocommerce-container {display: <?php 
    $display = get_theme_mod('woocommerce_productdisplay', '1');
    if ($display) {echo 'block';} else {echo 'none';}
?>; }
</style>