I think it is possible. How do you want to make this? Do you want to use the IDE or using Linux.
The camera uses Serial Communication and there are a couple of examples in the Arduino IDE and in for Linux using the GPIOs.
How are you going to store the images? You can use something like Re: opening image through webserver to send the images to a web server (Code: makers-examples/SendImagetoWS.js at master · MakersTeam/makers-examples · GitHub)
I think this other thread is going to be really helpful for you:Galileo help needed