Mosin,
It will work, but not be nearly as accurate as the KAB. If the light is locked to the incoming line frequency (50 or 60Hz), and the incoming line frequency shifts ever so slightly (which it does all the time, not by much of course (maybe +/- .2Hz)), but enough to be significant to a turntable's accuracy), you can see how the problem arises. You are now using your flourescent light (which may or may not be at the correct frequency corresponding to your strobe disc) to set the speed incorrectly. The power line is no place to look at as a point of reference!
The beauty of the KAB is that it operates off a battery - and it is easier to read than a garden variety "60Hz" strobe disc because of the higher operating frequency. All in all it is a very accurate device, and a worthwhile investment.
-Richard