Gyrd, I wouldn't recommend it. Home alarm systems and car alarm systems are different animals, and not well-suited to each other's applications.
One obvious difference is that home alarms need multiple zones not to be a nightmare to troubleshoot if/when a recurring false alarm develops. Home false alarms are more serious than car alarms, which largely go ignored in parking lots these days. The OP does not want to train his neighbors to ignore his alarm siren, and many municipalities charge heavy fines for continued false alarms. Aside from that, even the cheap home alarms have more features and versatility than car alarms for the last couple of decades.
Whatever the current system may be, if it uses RF sensor/transmitters to cover his/her windows and doors, it's unlikely that the system RF Receiver could be interfaced with a car alarm. If the current system is hardwired, it's almost certain to support multiple zones unless it's over 35 years old.
It's possible that a hardware store or Radio Shack DIY hardwire model control will carry a couple of input terminals for an Arm/Disarm dry closure switch--there were a number of cheap models that did that--and a garage door RF Receiver can be used to interface an RF key fob.
I was thinking about mentioning that yesterday, but I was waiting for a make and model number before I started listing all the possible contingencies from all the different makes and models. It's entirely possible that he already has a system that supports an RF Receiver and key fob,
The car alarm is limited yes. I doubt you can interface any RF door/window sensors to one anyway, and even if you could the car alarm would typically have 3-zones at most (Trunk, Door(s), Hood... and optionally a sensor to detect motion... ie collision).
The car alarm would be limited to what the op wants to monitor. If you only want to keep tabs on a couple doors, it's fine. If you plan to monitor all the windows and doors in a multi-floor dwelling then you need to spring for a proper home alarm with an RF keyfob.
Honestly, I plan to use one in my detached garage. If you build it simple, troubleshooting may be hard with multiple inputs, but if you put in the time, you can put in a circuit that site inbetween the car alarm and sensor and latches in position that will indicate which sensor went off. (You can use the output from the car alarm to reset the latch when you arm the system to allow exit from the premises)
I should mention that 'local' alarms like a car alarm wont dial out to Emergency services... and the false alarm situation can very well happen with an improperly installed home alarm anyway. In my region, if an alarm dials out, then I can be charged for false alarms.
If someone decides to call emergency services on my behalf because the car siren is going off, then I'm fine. This needs to be looked into by the OP though.