Not at this time.
Closing a Privacy Virtual Card prevents additional transactions from being authorized. (NOTE: Closed cards can't be reopened!)
Virtual card information is still kept accessible in the "Closed Cards" section of your account in case a refund or dispute needs to be requested in the future.
We're always adding new features, so it's possible that at a later time we'll have an option to hide closed cards. Keep an eye on your account for updates!