I know that in Magento it's probably not a problem since Magento uses different views for different languages but in WooCommerce which we tend to prefer for smaller retailer the way multilingual is handled it quite different. You need to use a plugin called WooCommerce Multilingual that integrates WooCommerce with the WPML plugin. So basically a product is created first in a language and then created in the other languages and linked together. The plugin keeps the stock and other product information in sync between the different translation.
My question is does your integration for WooCommerce has been tested in a multilingual setup with WooCommerce Multilingual cause we had serious issues in the past with this, it was working perfectly fine when adding products manually but when we tried to import products it really got messy and stock weren't syncing between languages anymore etc.
As you know WooCommerce does not natively support multiple languages and currencies. The WPML for WooCommerce extension that you are referencing is a 3rd party extension to handle multiple languages and multiple currencies in WooCommerce. Therefore, this is really one developer's "interpretation" on how to handle multiple languages and currencies, and unfortunately our WooCommerce Integrator does not work with it. I'm sorry.
Please let us know if you need anything else. Thank you.