It seems to be mixed.
Right now, demand on the power grid is highest during the daytime and lower at night. Most current EV owners charge at night, so they are using the system at a time when other demands are low. That places little to no additional stress on the system.
But.....
Many renewable power sources such as wind and (especially) solar generate more power during the day. There is a lot of wind power in Wyoming, for example, and it is typically windier during the day than at night there.
So.....
If we want to switch our power generation/collection over to wind and solar and dramatically increase the proportion of cars that are electric, then over the longer run we would want to switch to charging EVs during the day (because that's when wind/solar power is mostly generated). Get employers to install charging stations where their employees park. Charging stations in big parking lots at malls and airports and the like. A nice aspect of this is these places also make ideal places to install solar cells as shade structures. The car charges the battery off the solar system that is also protecting the car from sun and hail (I live in Colorado, which gets enormously destructive hail storms, the solar cells here weather them better than roof shingles and skylights do.)
Rooftop solar may turn out to be a big thing over the next few decades, I expect to see architects starting to include that in the basic design of all sorts of buildings, such as housing developments designed with more roof space facing south than north, arranging all the pipes and chimneys on houses so that they don't get in the way of solar cell installation, that sort of thing.