Hi Jem, good question. This is not something i have personally tried yet, but i do think what you are trying to achieve is possible. You will however require a specific approach as it is not a one click process.
Firstly see this article about P&D: https://help.k2.com/kb001782
From what i can read here you will have to upgrade to 4.7 as that will be the only release you can P&D from to K2 Five.
Secondly: K2 Five do not install the older development tools on a fresh install. The only way to keep the older designer tools are to upgrade from 4.7
So in light of this the best approach is to install 4.7 on your test server.
then P&D your current 4.6.11 application and deploy it to your 4.7 test server
Then upgrade that 4.7 test server to K2 Five.
Please remember you will not be able to open the older applications in the new workflow designer, only in the older workflow designers.
In order to work with the new designer, you will have to start new.
Looking into the future.
The new workflow designer is completely different from the older designers and also cannot currently consume the artifact or design files of those older designers.
I would recommend that you consider using the new workflow designer on any workflows redesigns or new workflows you plan to build out and use the older designer to tweak or fix bugs in your existing applications.This will help you minimize the number of workflows running on the older technology.