I don’t imagine there would be an issue with adding the microtonal device before your midi comes in, and thus gets recorded as the midi note information your record, or leaving the pyramid on either of the midi busses, there is no conceivable issue with applying the microtonal box to your midi output.
It’s possible that midi resolution isn’t fine enough to really get in between the pitches in theory, but if there is a midi device which can receive that data, and also send it, then I imagine it’s just a matter of producing the data, and recording it. Or at the very least converting it once it leaves the pyramid.
For in and out functions, I would look closely at the transmission of clocks. This could be a problem. Whenever a device is connected both in and out of a master clock there can (and almost always are) midi looping problems.
For the best possible results, I would look at the micro tuning box as either a controller on the way in, or a midi effect on the way out. This is sure to avoid the horrible double clocking heartbreak of midi loops.
This all said, I have not used this box, and so I don’t actually know for sure. But in theory, I don’t see why it wouldn’t work just fine.