Yes, I have the factory alarm and I had a remote start installed. I don't know the model number off the top of my head, but it's a viper remote start with a quarter mile range. It cost about $500 to have installed, and I have all the capabilities of the Toyota remote minus the cool beeping sound when you unlock it. I also have the ability to power the rear window up and down. I think if you hold down the lock button the alarm will go off.
Hope this helps. Just go to an auto shop in your area that is experienced. It's a complicated vehicle, you don't want somebody inexperienced working on it!