Yes, Current Version licenses can also be used on older versions of Geneious (from 6.0.3 onwards). Local Databases cannot be shared between versions, but individual folders and files exported in .geneious format can be shared between versions back to Geneious R6. Shared (SQL) Databases can be configured so that users on different versions can access the same data.
Geneious files from R6 onwards cannot be opened in version 5.6 or earlier. If the rest of your lab is on Geneious 5.6 or earlier contact email@example.com to discuss your options.
Post updated 4 April 2016