You mean standard, gasoline burning Prius hybrid + PV cells to power the home reduces CO2 emissions more than just driving a Tesla instead of the Prius, right?
Yes
The benefit to the grid depends on PV generation, cost of PV, and the fossil fuel that is displaced.
In Los Angeles, you can probably find a way to build a watt of PV for somewhere in the range of $2 - $4 , generate 50 kWh over it's lifetime, and displace fossil fuel that would otherwise emit 50 pounds of CO2 over the same PV lifetime.
If you figure that a Prius lifetime (in your hands or with successive owners) runs 200,000 miles,this leads to 100,000 pounds of CO2 emissions by the 0.5 lb/mile result I posted earlier. The PV offset then would be 100,000/50, = 2000 watts of PV that would cost $4,000 - $8,000. This does not take into account the CO2 emissions of the Tesla, which over the same 200,000 miles will be (according to the earlier post,) 60,000 lbs of CO2. So the Prius owner only has to offset the difference of 40,000 lbs CO2 to equal the Tesla owner, and build 40,000/50 = 800 watts of PV. That would work out to somewhere in the range of $1,600 - $3,200.
Since you probably paid tens of thousands of dollars to get into a Tesla, it follows that had the money been spent on PV instead the net CO2 reduction would have been quite a bit more. Probably somewhere in the range of 10 - 30 Prius owners with all the car savings of one Tesla spent on PV emit the same CO2 as one Tesla owner.
Needless to say, your answers will vary tremendously depending on your priorities, your POV, and who or what you use for comparison. Before you presume that I agree with your friend, keep in mind that Model S purchases are what allowed the Model 3 to come to market, and the Model 3 will push more people to install residential PV. The leveraged effect of your Model S purchase is difficult to put a firm number on but as a greenie through and through, I applaud your choice.
Cheers!