David:
To answer your questions, I tried it with my Rhodes 73.
I put it in auto mode, in which you play a note and the tuner automatically recognizes it. That works perfectly in the top octave. In the lowest keys, the tuner can be a little slow to recognize the note. (You may have to sustain the note or hit it twice to get it to identify and switch to that note. Once it identifies the note, it works perfectly.) That's not really a problem, but if you don't like that, you can easily switch to manual mode when tuning those keys, and press the button corresponding to the key before tuning it. So, the short answer is that it works fine in the extreme octaves.
It has a nice feature that helps you tune the extreme notes: by pressing a single button, you can change the motor speed, and display the tuning results in either a higher or lower strobe disc band. This allows you to tune an extreme octave and have it displayed in a middle strobe band, which is easier to read. (And if you have a need for it, it also expands the range of the tuner from its normal 8 octave range to 11 octaves.)
Pretty slick piece of gear...
Alan