Yes, you can. The Kinect has a depth sensor that uses an infrared laser projector with a monochrome CMOS sensor. So, with an assemble like this you can obtain image and depth according to your specifications under any light conditions on the raspberry pi. It is also possible to capture video data in 3D.
Now, to load the video for your use, you can use the existing driver present in the kernel like this:
Once you've done the above, you'll find a new folder /dev/videoX, which you can use to get a video like you would from a webcam.
Now, the main advantage with a Kinect is the depth, but if your kernel is older than 3.17, you'll need to install another driver. You can do that from here: https://github.com/xxorde/librekinect. And, If your kernel is 3.17 or newer, then you can toggle the gspca_kinect module's command-line depth_mode flag to just enable librekinect option. This is how you can do it:
modprobe gspca_kinect depth_mode=1
Lastly, both of these methods work great for me on Raspbian, which I'm assuming is your OS as well. :)