OK, maybe we were not as clear as I thought then. APM can monitor the components that are in languages we support. If Omnibus meets that criteria, you can monitor it. If not, then you can only monitor the Web UI with the core agent.
It is quite doubtful that Omnibus is a Java or .NET application. That means you can only monitor non-transactional data around the Omnibus environment, mostly via the EPAgent: log files, performance values you can poll, etc.
Those types of data are similar to the sorts of things you would do with Omnibus itself, which leads to the next item:
I understand that Omnibus has a self-monitoring extension and that ITM also has a probe for Omnibus. Those are probably the most insight you will be able to get because they are provided by the vendor.