Official comment
One of our Certified Consultants, Neil Kristianson, put together a video going through exactly how it works and posted it in our User Community. The short version is that per order, WooCommerce tells ONTRAPORT the following: Order number, First/Last Name, Email, Billing address, and Tax. Per line item, ONTRAPORT gets the SKU, item name, item price, and item quantity. It is not possible to track partner/referrer information through the plugin so if you are using WooCommerce and would like to have a partner program, you'll need to find a different plugin to handle that.
You can see the entire video walkthrough here:
https://www.facebook.com/groups/ONTRAPORTusercommunity/permalink/1354392964616880/