Logically, thieves won't enter a noisy house as they thought there are people awake inside.
I'm not 100% sure about this either, with the chance of being robbed is relatively uncommon, it's hard to do the test by myself since I sometime turned off the radio when I got bored, then go to sleep, then stuff happens XD
The good part if this is true is, the alarm will wake your sim, but not radios in another room. And the first 2 radios (I only got HELS + WA addition at the moment) are cheaper than the alarm so might be useful in the early game.
[Edited for profanity. Please read the forum rules and take care in the future. by wildredchild]