As technology stands right now, the answer is "no" or at the very least not make it practical to you. The reason for this is, an ELM327 OBDII adapter uses Bluetooth technology to connect with your phone. A Bluetooth connection is only good to ~100m unobstructed. When you start passing through structures and such, the signal attenuation starts degrading faster. With that in mind, I'm not sure if an OEM car alarm sends any sort of signal through the CANBus, but would bet it sends some sort of signal so as to shut the engine/ignition down so it won't start as well as lighting the lights and honking the horn (or whatever your car alarm does to make you realize it's going off).
On a separate note, there are aftermarket alarms which can pass information through the phone system or paging systems to alert you when there is an intrusion. I don't know how well they work, but do know there is a capability out there which can do this. A friend of mine a few years back had one in his car which he had a remote which would communicate through comms lines (cell phone signal) which he was alerted if his car was being broken into and which he could remotely start the car from just about anywhere he could get a cell phone signal. I wouldn't have used it, but it's out there.