If I feed the 1200x1920 LCD a display of 1024x768, will the LCD try to stretch it into a 1200x1920? Alternatively, will the 1200x1920 LCD put black bars around the 1024x768 display?
It depends on the screen. Most LCD monitors will allow you to use "centered timings" which will run non-native resolutions at the actual pixel size. That is to say, a 1024x768 image drawn on a 1920x1200 monitor will have a big black box around it, but it will look as sharp as the screen allows.
Alternatively, if the centered timing is disabled, a chip in the monitor will do the best it can to draw the image using the entire screen. Depending on the resolutions involved and the quality of the upscaling, this can really look like crap (or not, but generally so).
Aces high does support strange resolutions fairly well, although you may need to edit your video.cfg by hand. There are many posts that go into more detail than I will - suffice it to say, there is nothing to risk by trying it. I would bet that it will work, though standard disclaimers apply. :-)
FWIW, I am running AH on a machine with two 19" panels at 2560x1024 by stretching the desktop using ATI's CCC. There are utilities to do this with Nvidia products, though I couldn't vouch for them. Point is, it is possible to run AH on multiple monitors.
Hope this helps
