Q: How do I know if my account is connected to eBay's API or not?
A: If you set up and used eCom Syndicator or WooHosted for your repricing method, then you are using eBay's API.
If you did not, and your repricing method is, for example, the single File Exchange, the File Exchange + Chrome Extension or File Exchange via Authentication Token, then you're Not using eBay's API.