A recent study conducted in Sao Paulo, Brazil concludes that if the entire city went electric by 2035, then demand for electricity would increase by 40 million MWh.
As the study suggests, "every increase of 10% electric vehicles in the São Paulo fleet corresponds to an increase of about 2% of the electricity demand," according to Green Car Congress.
Additionally, every 10% increase in electric vehicles will lead to a reduction in total emissions in Sao Paulo of 1.3%.
Unfortunately, access to the study requires us to pay money, which we're not going to do, but the summarized findings presented above give us some idea of what would occur if a large metropolis converted fully to electric vehicles.
Source: Green Car Congress