No, you cannot currently copy a Campaign that is in any state, including published or ongoing. 

This is due to having live courses, phish templates and/or certain policies targeted to specific employees which would affect the reporting of the live Campaign.

As a workaround, if you wish to create a different version of a Fusion/phish template, you can copy/edit the relevant template, then save your changes, before recirculating this new version to a different User Group.