shields are just stacking daughter boards, and the number doesn't matter, it is what pins they use, if two shields use the same pin they cannot be used at the same time.
The number does matter; insofar as to the amount of current each shield uses...
you could just build a clock + keypad and have it turn on and off a FM radio via a relay, having the audio signals passing through the arduino is kind of wasteful anyway.
I can see where having an FM receiver chip could be useful; it would allow you to use the same interface to tune the stations, select (and save) presets (each person with an alarm can get their own station!), and you could even have the alarm slowly ramp up the volume of the station when the alarm goes off...among other fun things.
I wouldn't even bother using shields, a serial LCD just uses two pins, and using cables gives you more flexibility in design.
I do agree with this; sheilds can have their uses in prototyping, but when building a "final design", you are likely to put the Arduino in as a "standalone" on the PCB along with other components - no sheilds needed or required. I think shields were one of those things that seemed like a "good idea at the time"; and for prototyping/teaching, probably so - but they make no sense in a final design (nor does the Arduino carrier board, for that matter).
