Assuming by "reloading the box with EM 12c again", you mean deploying a new EM site on the host. If my assumption is correct, you will need to either:
(a) Redirect the agents to the new site
(b) Uninstall the agents and redeploy them
The only difference is that the server will now be 2008r2 Enterprise Edition as opposed to 2008r2 Standard Edition. Our admins require a complete rebuild to accomplish this but the machine name, IP and all the rest will be the same.
I am unfamiliar with Windows editions, but if "all the rest will be the same" means EM including its software library are kept intact, I will just check that the site starts, agents can upload, and do some overall health checking on the site.
The answer is yes the agent will work and be able to upload as long as you recretae the em with the same http address and port number. You will also need to use the same em repository database.
Thanks for all the answers. I'll be re-installing OEM as soon as our server is rebuild and giving it a try without re-deployment of the agents.
I'm resurrecting this for a follow up question, since I now have my server back and EM re-installed.
How do I reconnect the server with the agents without having to redeploy? When you go to add targets it ask for where to deploy the agent.