You can, the monitor would be set at 1920x1080 resolution to match the TV but you can scale it to full screen still. Problem is, the monitor and TV are physically much different size, and you only have 2 total. This would give you a terrible experience because the half of the game on the TV would be much larger than the half of the game on the monitor. Plus the bezel would be right in the middle of your view making most games unplayable.
You want 3 identical size or at least very similar size monitors, to keep a uniform appearance and to keep the bezels off to the side instead of in the middle.