Yes. Contact lists are saved in the system for future use. If you re-use or change the contact list after cloning a campaign, be sure to Save Draft before launching; otherwise, the Campaign will send to the previous list associated with the Campaign you cloned.
Please note that before a Contact List has been used in a Campaign, it can be deleted. Once a Contact List has been used in a Campaign, it can not be deleted. This is because the contact list information is used in quotas.
Please see the Best Practices for Campaigns Implementation for more information and naming suggestions.