Will it run in fullscreen? So far, I have only seen it running in a window or with a huge black border on modern systems.

It's the DOS version, and runs with DOSBox, so it can scale any way you want it to.
By default, it will stretch to fill your screen. If you're using a widescreen monitor, this can cause distortion, depending on whether the monitor supports aspect scaling or not. I recommend changing the graphic mode to "overlay" (use the Start menu shortcut, not the exe in the game directory). This will add borders to the left and right instead of stretching it out. It will still use the full height of your monitor, just not the full width.