I used to have that capability in Exchange. I would download RSS feeds using my outlook client into a folder. it would be synced using Exchange to my iPad and phone. So I could read, review and delete feeds on any device and have it synced. This is currently not supported as it seems.
Microsoft, please bring that capability to outlook.com (sync another type of message but emails). I believe this is a good way to consume feeds and stay on top of them across all your devices.