WC Autoship uses the Payment Token API introduced in version 2.6 of WooCommerce.
This means that if your payment gateway creates WC Payment Tokens, it will work with WC Autoship!
It's important to note, that the Payment Token API is relatively new to WooCommerce so not all plugins that integrate payment gateways (including those available from WooCommerce) utilize this new method.
Make sure to test this feature and don't assume your gateway supports tokenized payments.
If you're unsure, it's best to check with the plugin author directly.
What is payment tokenization?
Payment tokenization is a simple method for storing a customer's payment method (like a credit card, checking account or even a paypal account) without actually saving any real payment data on your website.
When a customer enters payment information on your site, your payment gateway receives and encrypts the data returning an obscure or "tokenized" key that is stored with your customer's data on your website. This "token" is completely useless on its own, but when submitted on a future checkout or Autoship order, requests the stored payment data on your payment gateway to be used as payment for the transaction.
Ultimately, payment tokens are easier to store, manipulate, and retrieve payment info in a standardized way. Payment methods saved using the WooCommerce Payment Token API can be managed from the user’s account settings and are displayed as options during checkout.