My question is at the end of this post, I just want to describe the situation leading into it first.
I need to migrate two 2003 Server based domain controllers to 2012 R2 DCs. The 2003 DCs are running in a very old (!) VMware GSX environment, so I have shut down the 2003 DCs one at a time and copied the file structures for both to a PC (I restarted the 2003 DCs to carry on business as usual in production). From the PC, I have used VMware Converter to update/copy the 2003 DCs to a new ESXi 6.5 environment that is currently isolated from the production network. Once I had the 2003 DCs up and running in the new ESXi environment, I created two 2012 R2 servers along side them and promoted them to domain controllers (using the excellent guides available on this site). Everything went smoothly and I'm now at the point of transferring the FSMO roles from the old 2003 DCs to the new 2012 R2 DCs.
My question is: At this point, can I shut down the old 2003 DCs that are in production on the VMware GSX server and then move the new environment I have created on the new ESXi host into production? How might this affect the servers and workstations that are members of this domain?
Since you have multiple DCs I'd use dcdiag / repadmin tools to verify health and correct any errors before moving on. Then also make the new ones GC (recommended), transfer FSMO roles over, transfer pdc emulator role to one of the new ones, use dcdiag / repadmin tools again to verify health, when all is good you can decommission / demote old ones. You can check demotion was clean / successful.
Just passing through... but beyond what was stated there are a few possible issues depending on the complexity of your environment, as well as the presence of legacy apps, which may cause a bit of a kerfuffle. If you have a complex/existing legacy app environment be sure to take a closer look at everything in the AD structure before change over.