It is possible, but it might not be the easiest method for controlling the video. What specifically do you need to do?
You can simulate keypresses by taking apart a keyboard (described at http://www.nastypixel.com/instantsoup/?page_id=19
) and replacing some of its keys with optocouplers (described at http://www.potemkin.org/cms/Pid/SimulateButton
) controlled by the Arduino board. Something similar should work for a mouse as well.
However, depending on what you need to do, it might be easier to have the Arduino board send commands over the serial port to the computer, where they are read and intepreted by a small program. For example, if you are (or can) play the video in Flash, then you could simply read the commands via a serial proxy. If you're on the Mac, you could probably use some AppleScript to read the commands (possibly via a serial proxy) and then send script commands to Quicktime or iTunes, etc.