There is no upgrade path from Windows 2012 Cluster to Windows 2016 Cluster.
You will have to do a migration. Which in effect is:
- Create a new cluster with one node on 2016
- Migrate services (including VM's and their related storage
- Once all is migrated, add in nodes
This means that a CSV volume/disk can only be on one cluster, and one cluster only. As you are migrating the answer to your question is; no the CSV volume/disk can only be accessible by either the node(s) of the old Windows 2012 cluster or the new Windows 2016 cluster node(s), but certainly not both.
There are migration processes defined by Microsoft, here
However for 2016 it lists:
Updated migration guides for Windows Server 2016 are under
development. Check back at this location for updates as they become
available. In many cases, the steps in the Windows Server 2012 R2
migration guides are still relevant for Windows Server 2016.
This won't detail a step by step process for what you are asking. There is a migration guide how to migrate from 2012 to 2012-R2 Cluster, this guide is largely valid, but you will have to adapt it to suite your migration from 2012 Cluster to 2016 Cluster. This guide can be found here
Furthermore, I would certainly not do this the first time on a production cluster, I would find a way to test this process. You could consider creating a Windows 2012 test cluster with VM's, then upgrade this test cluster to 2016 using the adapted process as indicated above. This would allow you to validate and fine-tune your process.