It'd require USB host mode. Which isn't totally impossible on the N9 so it seems. Still, even if that hurdle is taken, I don't know if the N9 supports the USB comm profile out of the box. Then there's the thingy with power. I guess the N9 can provide enough juice to get an Arduino running, but that might not be enough to power the various extras you hook up to it.

It might be possible to get the other tools running. And even the Arduino IDE might just run, as there is a working J2SE runtime for ARM which can run on the N9.

So yeah, my guess is it would be possible, given enough effort. But if it's only for the "just because I can!"-factor, it seems to me this would be way too much effort.

Bluetooth might be a better option - and indeed I'd like to know if that's going to work easily. It would allow for very easy communication without other requirements, once that communication channel is established. But if you're planning on using it on your home network, an ethernetshield is probably by far the easiest solution. You can communicate using HTTP, which makes it possible to use it directly from QML.