So does this problem actually surface when a lens is attached? Last I checked, it's tough to take pictures when the body car or lens cap is blocking all the light to the sensor.
Yes, under very specific conditions. Namely the subject you're shooting must be lit at EV 1 or darker (that's 1/4s f/4 ISO 3200, or some equivalent exposure). If the subject is brighter than that, I can't (at least on my body) produce any error in metering by switching the backlight on/off, and have to step up to shining a 100+ lux flashlight on the top LCD.
Moreover, I've tried to reproduce in the "lab" a "concert" like scenario where the camera was in the dark pointing at a slightly brighter subject with a flashlight (simulating a spot light) shined over it. Again, so long as theh subject was lit to better than EV1 I couldn't produce a change in exposure (though there are quite a few more variables here than I would have liked).
http://www.cameratown.com/reviews/canon5dMKIII/light_leak.cfm
I find it hard to take anything that camera town has to say very seriously, after his comments about removing your eye from the viewfinder affecting the metering, given that's normal and expected behavior. Moreover, I find his claims that his 60D doesn't do it to lack voracity at best, doubly so given the lack of control in his tests.
A light leak somewhere in the body would be an issue for those of us who do shoot in darkened environments like museums without tripods (some museums don't allow tripods), or night-time photography, in that while there are times we can take the time to make sure we get that shot, there are other times where we can't take a couple minutes to get the shot right, and have to take it "on the fly".
This is where the camera's automatic metering comes into play; and if there's a light leak that throws this into doubt...
I don't see how, by the vary nature of this problem, if you're composing the image though the viewfinder, there's no reason to have the top LCD on. Moreover, so long as whatever you're photographing is lit to better than EV1, there doesn't appear to be a problem—at least in my testing. Finally, so long as you don't have a super bright light shining on your camera lighting you/your camera to an appreciable level over the subject material, again, there shouldn't be an issue (at least there wasn't when I was testing this with my camera).
Which brings me back to the "concert" scenario (which too could be applied to your museum scenario, that is a dark environment with very bright lights shining on the camera directly. How accurate is that really though? I can't recall the last museum that I was in that shone lights directly on the patrons while keeping the exhibits comparatively in the dark.