The first stats I was able to find indicates that, at least 5 years ago, they did help.
This site has the table I’m going by:
To find the table, open the above URL and Click Edit, then Find and query for “Effect of passive immobilizing antitheft devices on theft losses”
It appears that depending on the vehicle in question, the effect ranges from substantial to statistically insignificant.
In the case of the Nissan Maxima, circa '98-99, the “Claim frequency per 1,000 vehicle years” goes from 7.8 to 3.0 when the system is added.
In the case of the Ford Ranger 4x4, circa '98-99, the “Claim frequency per 1,000 vehicle years” goes from 2.0 to 2.0 when the system is added.
So, basically no change at all in that vehicle.
I didn’t see any links that answer MY question: “Now that more cars have this kind of system, is that lowering car theft over-all?”