We don't have full Airbnb support yet, but it's something we're investigating. We added that system listing site as a way to manually tag inquiries and bookings to Airbnb for conversion tracking. For now, you still need to communicate through the Airbnb site.
We're planning to add support for walled gardens like Airbnb and FlipKey payments so inquiries will come in to OwnerRez and you can respond and manage them like other inquiries. You won't be able to send quotes or accept payments through OwnerRez since Airbnb and FlipKey do that through their system, but once this is done you'll be able to communicate through OR and have inquiries and bookings automatically created rather than having to work in their sites directly like you do now.
I don't have an ETA on that feature yet, but I'll keep you posted as things get closer.