I know you didn't ask about Ubuntu 16.04, but I can confirm that the PS2 Eyetoy camera works out-of-the-box on that version. I checked to see if it was detected with:
lsusb
which returned:
Bus 002 Device 006: ID 054c:0155 Sony Corp.
and then used Cheese Webcam Booth to test the picture.
PS. These cameras have a manual focus ring on the front, took me a while to realise.
According to this website, that camera will work out of the box. You should just be able to plug it in and use it.
You can test it out by installing the program Cheese, available from the Ubuntu Software Center.
A more recent post (2014) states that the camera works perfectly fine on 12.04.
I know you didn't ask about Ubuntu 16.04, but I can confirm that the PS2 Eyetoy camera works out-of-the-box on that version. I checked to see if it was detected with:
which returned:
and then used Cheese Webcam Booth to test the picture.
PS. These cameras have a manual focus ring on the front, took me a while to realise.