There are two types of delete, Soft Delete after deleting a customer it will go into trashed customer listing ( Customers > Trashed Customers) and that customer will not be able to login into its customer portal. But that trashed customer still can submit tickets.

On Trashed customer page two options are provided Restore and Delete Forever. On deleting forever the customer will be deleted along with its data i.e tickets. This is called the Hard Delete. After hard delete, if the customer submits a ticket again then it will be treated as a new customer.