No, not at this time. Our current support enables new customers to create a new ShippingEasy account and access it from within Bigcommerce.
If you'd like to create a new ShippingEasy account, you can sign up here and follow the steps in our guide to install ShippingEasy as an app within BigCommerce: How to: Integrate using Bigcommerce Single Click Install with ShippingEasy.
Note: if you're setting up a new account, you'll need to use a unique email address as your account login.
For more information about using ShippingEasy as an app within BigCommerce, take a look at our how-to guide here.