As far as I recall, the immobiliser doesn't allow the car to turn over at all, so it must knock out all the ignition at the very least, additionally if you open the door without disabling the alarm it's triggered after a few second interval, ie it gives you a few seconds to press the alarm button on your keyring before it goes off.
In the Rover equiped car the alarm was fully integrated with the engine control system.
In addition to the horn going off the car won't start if the alarm is set. Which leads to some problems since the two halves of the alarm can get out of sync and lock up. Exactly what happened to me. Had to tow the car home, call the UK and luckily they suggested a way to resync them without the special reprogramming box that no one in the US had. A real close call.
No idea how the Toyota will work, but would expect it would be about the same.
Not that either are much good against the problem of someone wanting to break in given the soft top.
Or stealing the car even. Heck at 2000 pounds four guys can pretty much carry it away.