Yes and No.
Yes its possible, but no. I highly advise you not use the camera for that purpose.
How long of a live video feed are you planning on doing? The main issue is that eventually the camera will overheat and turn itself off. While this is not bad for your camera because its a built in safety measure, its not advised. These cameras can shoot video for a long time but if you are running a live feed off the camera into a computer through the cameras live view function then the cameras will not be likely to engage its safety functions to protect itself. I will warn you that eventually after extensive video and live view use of the camera that it is possible to wear the sensor out but it takes a lot of use before that happens.
To use the camera for the purpose you have inquired you just need to use the canon software to hook the camera up to your computer and switch the camera to live view. there are a few guides to step by step instruct you on how to do it and get the feed somewhere such as skype.
I have had a friend use his 5D2 as a webcam in skype for a few minutes.
all i have to say is use some caution on how long you use the camera for a live video