WooCommerce API in Elixir

This is totally general question. I’m just starting to learn Elixir so it’s kinda question about right path.
WooCommerce thanks to many plugins resolve problems with integration with so many services. My choice is mostly taken because of payments providers but not only.
Does it make sense for you to make CMS/static website in Elixir and integrate WooCommerce into it ? Would it be painful? Is someone working with Elixir and WooCommerce ? I would like to have “account feature” in my elixir app, how then I could be authenticated in my WooCommerce app at the same time.

Like I said it’s general question. I’m just trying to understand which way should I choose. I want to use exisiting ecommerce solutions and take advantages of elixir.

On the side question. Would it be wise to use Wordpress to generate static content and then serve it by elixir and attach dynamic solutions like comments by using elixir ?

Thanks in advance