I wouldn't recommend it. All the pieces have similar harmonic colour. Not only will you get tired of it. But even worse, the pieces might start to sound connected while they have nothing to do with each other, obviously.
Playing in period order is stupid. You need to consider the music and decide for yourself what you think is a order you would like. I would play Bach WTC fugues, detached from the preludes, and follow it up with something modern like Barber or Medtner.
Playing Bach before Beethoven just because Bach was born first is senseless. It does not say anything about the music, you need to consider the music only. You might even have a neo-baroque fugue inbetween two atonal pieces if you blindly apply this rule.