With the caveat that actual implementation of any security features may vary by region....
I may be wrong, but I believe the native security system in gen5 CRVs is designed to prevent theft.. NOT alert for theft.
By this I mean that if someone forces open a door, it will trigger the immobilizers, not sound alarms. The car beeping will not cut it. Firing off the horn might, but I do not believe our CRVs do this straight from the factory.
With my CRV.. I elected to purchase the after market security system that my dealer installs on every vehicle on their lot (this is there theft prevention methodology, and the offer to keep it active when you purchase... for a large discount on the retail cost of the unit). This particular system DOES initiate a temper tantrum via the horn and lights in the vehicle. You can literally set it off by dropping a tennis ball onto the hood of the vehicle from about 3-4 feet above the hood.. and it will go full tilt horn fest, lights flashing, etc... for about 30 seconds. An accidental nudge with your body on any body panel will trigger a similar effect... so I doubt a thief would ever hang around long enough to actually force a door open (actual experience while moving around inside my garage

).