In regular picture mode? That is an optical image, not an electronic one.
You can take photos in Live View mode. Then the connection is the same as in video, and you can output it to a monitor via HDMI.
It also is possible to shoot still photos "tethered" in the regular photo mode. Basically you hook the camera up to a laptop or other computer via USB or Firewire. Then you control it with a Canon software program.
What you actually view on the laptop is a test image that you take, by releasing the shutter, or the actual image after you take it. Unless you are in Live View mode, then it is just like using a monitor.
Cameras that use an EVF can output the image at any time, but they are essentially like the Canon in Live View mode. No mirror to relay the optical image, just the electronic image read off of the sensor. On the Canon you have the choice or either/or. Never both at the same time (when the mirror is up to get the sensor image,, there is no optical viewfinder.)
