Looking at the code….no….which is insane. The plugin saves if it has been sent to Shippit with
update_post_meta($orderId, '_mamis_shippit_sync', 'true', 'false');
but it doesn’t save the actual tracking code.
Currently best you could do is some hockey stuff to pull the code from the order comment. I hope they updated this at some point but I doubt it
$orderComment = 'Order Synced with Shippit. Tracking number: ' . $apiResponse->tracking_number . '.';
$order->add_order_note($orderComment, 0);