Tonight I tested this.
1. xbox360† -> microsoft HD component cable -> VDIGI -> VGA cable -> G2A130*
results: 720p works and looks good. 1080i works, but every other line jiggles back and forth a pixel or two
2. xbox360† -> microsoft HD VGA cable -> G2A130*
results: all resolutions work except for 1920x1080, at 1080 it simply defaults back to 480p automatically
3. I am going to order a simple component-to-VGA cable like jonjandran has, and test this out, results to come in a few weeks
Now I hate to be the bearer of bad news, but while testing I found 2 very disturbing things.
The red xbox360 displays is washed out, and the black xbox360 displays is not exatctly black. I tested this with setup 1. and 2. on both my projector and viewsonic vx2000
This is PIP mode on the projector, xbox360 on left, dell laptop on right

This is PIP mode on the projector, xbox360 on left, dell laptop on right

This is a veiw of the hailed vx2000, excellent black levels, the top and bottom bars are true black, the middle is the "black" xbox360 displays (this is in 720p mode, letterboxed)

I can only assume the terrible black and red levels apply on regular TVs and HDTVs also. I am going to test on my roomates 47" CRT samsung rear projection now.
EDIT UPDATE: Tested with component HD cables strait into TV. I tried to take a picture but I am not good at taking pictures of TVs, so take my word for it. Black level was acceptable, but not as black as my VX2000, and red was very RED, I was quite impressed actually.
So now I am going to test the laptop through the VGA port on the G2A to see if that is the issue.
EDIT 2: I put the VGA and DVI output image from the laptop side by side in PIP mode, black was black and both reds were the same (my projector doesnt display red perfectly anyways, but it was still redder than the xbox360s red)
*Bought this from Dobie in November I think it was, this is not the original minoten controller.
† updated through xbox live to current version of the date of this post