Yes, multiple payment methods can be stored in Fusebill for a single customer including credit cards, or bank accounts. However a customer can only have one default payment method.
If the customer has auto-collect enabled, the system will automatically charge the default payment method when an invoice goes from Due -> Overdue.
If this payment method fails, it will not attempt to collect from secondary payment methods. In order to do this, you would need to set one of the secondary payment methods to default, then manually process the payment.