Hmmm.
[IG]http://i33.tinypic.com/2ur5h1g.jpg[/IMG]
It could (and should) work, but it really depends on the specs of your buzzer and the water - not to mention that your electrodes will be pretty charged up the whole time, which means there will be plenty of oxides and other chemical impurities on their surface, adding even more randomness to the outcome (and possibly toxic metal ions/compounds to the water - goldplated or stainless steel only please!). As you can see from the site above there's also the factor of how much of the electrodes are covered in water. It's a complete crapshoot, to be honest, and there's no way to calibrate the circuit. Keep in mind that this is a great way to produce oxyhydrogen, which in confined rooms may accumulate over time. It's a comically small risk, but it's there.
The parts needed for a rather reliable sensor are far less than fifty cents per "watchdog circuit".
Here, look at
this for example (ignore the ads and whining).
...or
this.
However, may I suggest a far less dangerous method? A float switch. This one may cost a teensy bit more (unless you build it yourself) - but no current will ever come close to the water, eliminating any possible danger.
At last, as a curiosity:
[IG]http://i37.tinypic.com/2zpmrfp.jpg[/IMG] (
source)
The sugar cube melts away when in contact with water. This is used to trigger a switch. I do believe that idea is awesome in its simplicity. :lol