That is not a tangent at all. To answer your question, I have seen the rotor influence check performed but have never seen it detect a broken bar. Specifically, that is not to say that it failed to detect a broken bar when it was present, but to say that I haven't been fortunate enough to see it used on a motor with a broken bar. (Yes, in the repair business a broken rotor bar is a good thing...)
However, based on the explanation given me about how it works and seeing it in action, I am confident that it is a valid test. You can actually count the # of bars on the rotor by performing this test!
Another useful feature was the online plotting of current and voltage over time. In one case, we were plotting the current waveforms of a 3 phase motor on a belt driven 2 cylinder compressor. The current waveforms were seen to "pulse" with a period equal to about 5 or 6 electrical cycles. At first we thought it was the belts "tensioning" as they could be seen to pulsate with some regularity. However, we soon realized that the belts were not the cause but another symptom of the same cause. It turns out that we were able to correlate the current pulses with the compression strokes of the cylinders by taking into consideration the pulley ratios and assuming that the motor was a 1-delta winding and that the cylinder strokes were 180 out ( in the reference frame of compressor rotation). That was pretty neat! (for me at least, you know what they say: "simple pleasures for simple minds...."

. This implies that this can be useful for evaluating loads as well as motor perfomance. For example, knowing this to be true we could now check for a weak or dead cylinder based on the current pulses during the compression strokes.
Another useful (and neat!) online tool was the plotting of the starting current. Really, the list goes on.
Have you had a chance to evaluate one? When we were considering purchasing one and the rep wanted to do a show and tell, we did so by testing a few motors in the shop, both offline and online. After all, the proof is in the pudding. If you haven't tried one out yet, contact them and set up an in-plant demo.
If you are interested, I may be able to put you in touch with someone who can set that up for you. As well, I am open to discussing these features or others if you want to know more. I will say that if you get really technical I will probably have to call our PDMA consultant for help, but that is no problem.
Have a nice weekend and a happy holiday.