We have a total eclipse of the moon in March or April, and I'd like to get some good footage. I currently only have the standard 16x lens, but if I bought the Canon EF Adapter I could attach my EF 70-200mm f/2.8L IS USM.

I figure that this set-up would give me a closer shot (although I'm not sure how much closer), but any thoughts on light limitation using something like this and shooting at night?

The moon is lit by sunlight, just like day time earth. So aperture and shutter setting for nominal exposure would be very roughly the same as shooting a similar landscape on earth during the day. Do some shooting in advance to test what works to produce the effect you want, and hope for clear skies.

The EF adapter and lens combo you mentioned should give you a field of view about the same as a 500-1540 mm zoom lens on a 35 mm still camera.

First thing: shoot full manual and completely ignore your light
meter (zebra stripes are 100x more accurate in such conditions).

I've shot the moon with my standard XL1S + standard 16x lens
a couple of times, see a sample shot here: www.visuar.com/DVi/moon.jpg

That's maximum zoom on a moon with a bit of clouds in front of
it. It was shot with either -3 or 0db gain (definitely not more!).
I'm unsure of shutter speed or iris, but it shouldn't be too hard
to figure those out.

On a clear night the moon is giving of massive amounts of light
if you zoom in! As Don also said, do some test runs first.

I've used my XL1 with EOS adapter and 100-400 IS. Great moon shots.
With and additional 2X converter you can almost get inside a crater.