On one hand, I think people underestimate how much energy our grids demand in a 24 hour cycle. The amount of lithium it would take to handle an unusually cloudy week would be astronomical.
On the other hand, one of the ironies of electric cars is that they are one of the least effective uses of battery capacity. A Tesla with a 60kwh battery is probably touching less than 20kwh of capacity every day.
So theoretically if you use the batteries for grid storage and actually cycle them regularly from 80% down to 20%, the battery capacity would be well over 2x - 4x more effective at offsetting carbon sources. (Even more so if you are offsetting worse sources like coal).