I believe you can interrogate whatever controls you need. It is certainly going to require more work than using the connector.
The best approach in your situation will be to perform interrogation on the controls you require and write the automations to perform those actions. Someone on the forum may have written something generic they can share. I personally have not had any of my customers use OWA versus the desktop client, so I do not have an example to provide. If you do have specific areas that are of concern though, post those and we might be able to assist you with a specific area you can't interrogate or need assistance with.
You are correct in that there's nothing specific created to access OWA. For that, you would treat it like any other application and perform the interrogation and write the automations for it.
I did a quick Google search and could not find anything immediate for help with OWA as most of the interaction Microsoft intends for Outlook is through the application (using Interop like the connector does). You might find something with a deeper search though.