"mirrors what is on the display"
As I have the T3i I thought I'd check that out but I see I need an adapter from the camera to HDMI. I'll get that by next week.
But my guess is the HDMI output would be just the image and not what I see on the LCD. What's on the LCD with menus and overlays might not show on HDMI. But I'm just guessing. We'll see next week.
Are you telling us that Canon does not answer such questions?