Using a simple RC or RL filter as both high pass and low pass at the same time
If I had a simple RC or RL filter, and I connected both the high pass
  output and low pass output to the same output, would the overall
  output be roughly the same, assuming high efficiency components?


No, because you would end up with a band-pass filter if the capacitor output and the inductor output were joined: -



The above becomes this: -



R in the above diagram would be the parallel combination of the individual resistors from the RL and RC stages. The inductor and capacitor would be joined electrically and this means that the potential for energy transfer between L and C is 100% i.e. you get a resonant tuned band-pass filter.


  if I was to connect them to seperation outputs, let's say to two
  identical speakers with infinite and flat frequency responses,, would
  there be much difference between the input and output signal?


On the face of it I would say that at a distance from both speakers you would hear a flat sound i.e. spectrally flat. You could place a mono microphone equidistant from both speakers and, assuming the 3 dB points of each filter was the same you would reconstitute a flat signal.

It would be the same if you took RL and RC filters and fed each to a mixing desk - the signals could be added passively i.e. there would be no L and C interaction.