Yes, this can be done. In fact, the Mac OS has supported single desktop on multiple displays for more than 20 years.
If you have a video card with 2 connectors, and you hook up two monitors, you should get a spanning desktop automatically. The "Displays" system preference will let you set the position of the displays relative to each other.
I currently have two displays on my Mac, one a large 19 inch and the other a smaller one. The smaller one is set to a different resolution, and there's no problem at all.
Really, it's easy.