antenna's don't just work that way. they are designed to pick up a certain range of frequencies and I don't think your alarm system will be in that range
Your built in antenna is cut to serve FM radio freq's. It will not be an efficient match to your transmitter/reciever. It could even burn out your transmitter in your alarm.
You could add another antenna that is the same length as the one you have now, or if you know the frequency you can just find an antenna for that frequency range. Use high quality 50 ohm antenna cable and keep the cable length short and you could connect to your new antenna.