Not really. You actually may have other legal requirements to keep the data but you shouldn't use it for daily business because of GDPR. Imagine banks and long closed accounts.
Moreover, technical backup solutions, where only a very limited set of people have access, are fine. If you store DB backups, you don't have to rewrite or delete them because a customer that used your service for a week decided to ask for deletion under GDPR.
That's a different part of GDPR: purpose limits. Deleted or not, you can only use data for an approved consented purpose that is mapped to that data item.
Moreover, technical backup solutions, where only a very limited set of people have access, are fine. If you store DB backups, you don't have to rewrite or delete them because a customer that used your service for a week decided to ask for deletion under GDPR.