is it possible to set camera to orthographic in fps shooter

so I was thinking about making a flatland type game and it seems to me after a couple of days experimenting with unity that it would be a good engine choice.
I have made a simple mockup but when I set the camera to orthographic view everything turns upside down and distorts when I move around.

If you want to create a Doom style game use billboards(billboards are basicly quads with a texture, always looking at the camera).