You can integrate Woo Commerce with Ontraport with WP Fusion. That page explains the basic functionality that WP Fusion provides.
WP Fusion does include adding a tag for abandoned carts – see this article. You would then use a Campaign in Ontraport to act on the tag being added to the contact.
ONTRApages would not be used as the shopping cart itself in Woo Commerce. If you need a catalog/storefront type environment – you’ll use the Woo Commerce shopping cart’s code and pages. You’d use ONTRAPORT Pages for thing like lead generation pages and maybe a sales page with a button that leads to your shopping cart pages.
I hope I explained this well enough for you. Please let me know if you have any questions. Several of our customers are using Woo Commerce with WP Fusion, and you can seek them out for their experiences by joining our Facebook User Community. The developer of WP Fusion is also active in there.