Hi Sarah,
Definitely, that customer info can be exported to your 3rd party email platform. The question now is, at what point are you retrieving that information from the customer?
Normally a customer can opt-in to the newsletter in the checkout process. In that situation, a order related webhook would be the ideal solution.
The 'customer enable' webhook could work if you're making users create their own accounts and you want them to opt-in to the newsletter at that point in time. Note that this isn't provided by default in a Shopify store, and requires some liquid customization to get the opt-in information at that point.
So, to summarize, you'll be able to do what you want, and the right webhook to use will depend on your specific use case.