Need formula for core detection
The shaft would have to be ferrous to disturb the magnetic field of the coil so what your proposing wouldn't work with aluminum.

If all you need is water flow:  Its possible that with a coil around the feed shaft or any other component which water flows through that you could detect a disturbance in the coil as a result of the moving water (which contains iron among other impurities in most locales).  Your sensing circuit would have to be quite sensitive.

All that being said, if I were you I would just put a single flow meter on the system back at the water source and compare the amount of water flowing to the amount that would be flowing if all sprinklers were operating correctly.