Yes, you can!
By default, Ordoro posts tracking to WooCommerce by adding a note to the order in WooCommerce with the tracking number information inside that note. Ordoro will then mark that order as completed. Here is what the note looks like.
With the latest version of WooCommerce (2.2), WooCommerce will email the customer that note. Ordoro also writes back separate notes for split orders, and will close the order out when the full order is shipped.
Ordoro also integrates with a plugin in WooCommerce to post tracking back to the Shipment Tracking field in WooCommerce. Click here for details on this plugin integration.