The alarm and anti-theft system have nothing to do with the radio, in a Blazer or an Impala. If your friend had ignition problems after installing a radio, then something was mis-wired.
The Impala is equipped with a GM data-bus type radio, so unless you use one of the expensive adapter modules or a relocation harness, you'll lose all audible warning chimes when the radio is removed. But even if you don't use a data bus adapter, you shouldn't have any problems with the alarm or anti-theft system.