The AirPort Time Capsule (the official name, with my emphasis added on AirPort - see below for the reason), runs NetBSD, according to the Examples of use section for NetBSD on Wikipedia. It cites two sources - one being an answer from superuser.com (not very useful in this case), and another an article on wifinetnews.com, that states:
A source unconnected with Apple provided convincing proof that the AirPort Extreme uses NetBSD as its embedded operating system...
The AirPort Extreme Base Station, AirPort Express Base Station and the AirPort Time Capsule all run the same firmware (that's why the AirPort in all the names). This can be seen in the firmware downloads available for these products - it's the same download for all these devices. Of course, nobody has jailbroken these devices yet, so we do not know if or how the installation process chooses specific bits for the underlying hardware. But the OS cannot be different with the same firmware download (it does not make sense for these devices to have such a scheme).
See the recent AirPort update 7.6.4 page for understanding the above correlation.
I've plugged in a Drobo S into the USB port on an Airport Extreme when I needed fast and dirty file sharing. It worked fine. It was only for a week, but I didn't notice any sort of unusual behavior.
Once you've done the initial setup/config via the Drobo interface, the drive acts just as standard USB drive. It's not the fastest thing in the world, but you're limited by the USB 2 anyways, so your experience regarding speed will depend more on your actual usage.
I see this every few months and all other features of the device seem to work fine when it happens. The short answer is a restart has always fixed it for me, either from the Airport Utility or if you must by cycling the power.
Best Answer
The AirPort Time Capsule (the official name, with my emphasis added on AirPort - see below for the reason), runs NetBSD, according to the Examples of use section for NetBSD on Wikipedia. It cites two sources - one being an answer from superuser.com (not very useful in this case), and another an article on wifinetnews.com, that states:
The AirPort Extreme Base Station, AirPort Express Base Station and the AirPort Time Capsule all run the same firmware (that's why the AirPort in all the names). This can be seen in the firmware downloads available for these products - it's the same download for all these devices. Of course, nobody has jailbroken these devices yet, so we do not know if or how the installation process chooses specific bits for the underlying hardware. But the OS cannot be different with the same firmware download (it does not make sense for these devices to have such a scheme).
See the recent AirPort update 7.6.4 page for understanding the above correlation.