Would it be posible to compile kinect drivers for carambola?

I don't see why not.
Kinect drivers have been compiled for other ARM based SBC's like the BeagleBoard (there's an interesting project using the Kinect and a BeagleBoard on a Quadrocopter).
I just wonder how much you could do with the Kinect Data given that your memory and processing power are rather limited compared to the BeagleBoard. It should be more than enough to stream depth and image data from the Kinect over WiFi though.

OpenWRT makes starting with Carambola and Kinect easier. There's a libfreenect package in the OpenWRT OPKG Repository which installs fine on Carambola. The driver seems to work as it brings the Kinect to life when it's plugged into the USB Port.
So you'd now be left with the task of writing your Kinect application based on libfreenect.
I'll probably look into that at some point in the future.