Sounds like a fun idea. I imagine any resistance to the pedals would extend a derailleur past it's capability and break it, thereby defeating the purpose of riding with a fixed gear in the first place. Also, the distance between the fixed cog and the edge of the freewheel seems like the chain would get dropped inbetween before it shifted successfully. So, yes you could assemble it but it wouldn't be practical or usable.
Have you seen retro-direct drive bikes? I'm sure you would like those.