If you have an understanding of the circuit and of electronics, then it would be easy to add monitoring. One of the floats would turn on the well pump when the level falls so one could couple to it to sense the voltage or current. From that, it becomes a matter of how long the signal would be present and then use logic that alerts if the time has been exceeded.
Personally, I would not tie into the existing float system but rather put in a separate system. One could monitor the pressure at the bottom of the tank rather than use a float. There is .43 PSI for every foot of water.