The million dollar question is how you would be able to pass the design data back to WooCommerce?
In WooCommerce, a product is like a WordPress post, or more precisely a Custom Post Type.
You can create products in WooCommerce through the REST api just like you can create posts in WordPress through its REST api. I tested it with Postman (api client) and it works. Problem is, that you will need to authorize the client (the app running in the visitors browser) full read-write access to the shop. Which seems highly unsafe. So I ditched that idea.
I am now thinking of using a form to get the data to WooCommerce. Gravity Forms (WordPress plugin that I use to make forms) has "post fields" that lets users create create post content by filling in a form. If the custom post type is a "product" and has a price (meta key "price" with a value ) it can be added to a cart.
Or, maybe I could create a product "custom board" which already has a price, shipping class etc. in WooCommerce and let the user give his creation a name, design the board in the configurator, add the images and click the add to cart button.
Might work, although it will require action from the user, specifically to handle the images.
This post mentioned that they integrated it, but not likely to your detailed level. construct.net/en/forum/construct-3/general-discussion-7/construct-3-as-app-making-soft-125202
So it should be possible, although probably way out of my skillset.
I will run a test with the post-creation form and the product add-on idea. If anybody has a better idea, I'd love to hear that.