If you are capturing from a Canon you won't be capturing a clean camera output but the image you see in the viewfinder, ie superimposed camera info etc.
I believe the only HDSLR a clean camera out can be captured from via HDMI is the Panasonic GH2.
BEFORE it was recorded? As in a raw feed from the camera? As Phil said, you can't do that. Not with the Canon's anyway.
AFTER it was shot? Zero benefit in any way. You'll be converting to ProRes, and will have to do it in real time, manually. And you will not get any usable timecode. If you take the card and use the Log and Transfer method, you still get ProRes files, but you also get a reel number and time of day code, and the ability to re-import if you lose a drive or want to revisit a cut.