Understanding Impedence when modifying a spring reverb
Would I be able to run the output of my keyboard into the input of the
  reverb and then just run the output of the reverb into an XLR mic
  input on my mixer to amplify the signal back to the proper level?


That would work but it would sound awful. The reason why is that a spring reverb is just the pure "reverb" section of the overall sound a musician would expect. Typically the output from the spring would be mixed with the original sound at a level of maybe 5% to 10% - that would then produce a "reasonable" reverb sound.

So you will need an op-amp mixer on the output to subtley mix the spring output with the original sound. This now means you have a powered output buffer and you might as well use a powered input buffer to drive the spring and thus present a more reasonable impedance to your keyboard's output signal.