If anyone else is having problems with Google Checkout not sending customer update notification emails this is what fixed it for me:

in admin/orders.php (after editing for Google Checkout), around line 112, just before the first "END GOOGLE CHECKOUT" change

PHP Code:
$customer_notified = isset($customer_notified)?$customer_notified:'0'; 
to

PHP Code:
$customer_notified = '0'; 
Around line 116, change

PHP Code:
if (isset($_POST['notify']) && ($_POST['notify'] == 'on')) { 
to

PHP Code:
if (isset($_POST['notify']) && ($_POST['notify'] == '1')) { 
No promises it'll work for you, but with these changes, I now get the green tick and email sends again.