One concern would be that if it acts like most X10 camera power supplies, it would turn off if it heard an X10 "on" command within a "group of four".
Say it was set to respond to A1.
If a "A2 (or A3 or A4) On" was sent, it would turn off.
Also, it only outputs 80 milli-amps at 12 volts DC. You would have to be sure the siren doesn't draw more current than that.