In my opinion, Enterprise Manager Cloud Control server should be able to connect My Oracle Support. You may use a proxy if you don’t want it to have a direct connection. Sometimes, security policies do not allow your Cloud Control server connect internet in any way. In this case, you can use it in offline mode, and still can use self-update and patch management features.
First of all, you need to activate “offline” mode. Enterprise Manager Cloud Control will not switch to offline mode when it can connect to My Oracle Support. You need to switch it manually. Click “offline patching” under the “provisioning & patching” menu. Select “offline” for connection mode, and click “apply” button.