Yes. There are two ways to use the plugin:
Use the Fast Cart as an extra option for customers. Customers click the cart icon to access the Fast Cart and can checkout from there, or they can use the regular WooCommerce checkout page.
Replace the entire WooCommerce checkout and only use the Fast Cart. You can choose to replace the Cart, the Checkout or both. This means that whenever a customer clicks on a link to the cart/checkout, it will open the popup cart instead.