Yes they can still do it using queries. You need to ensure the Test Case name are unique and not repeated in another project. If they are unique, they can first get the list of instances in previous project and write into new project referring to Test Case Name in new project. this will create the instances in Test Lab for those cases and Test Sets..
are you expecting to load Steps or Runs? that will be complex but still DBA can do it..
are you expecting to load Steps or Runs? that will be complex but still DBA can do it..