Not if you program the cars to charge overnight. It requires more smarts, and grid interaction, but the cars could be made to obey instructions from the grid operator.
Individual EV drjvers can set the start time for charging. It's polite to set it for sometime after midnight. This isn't fancy smart-grid stuff, just a new kind of basic common sense that will emerge as EVs get more popular.
When pitting politeness against convenience (having the most charge in your car as is possible at any moment in time, in case you need to use it for something unanticipated), I don't have high hopes.
To really incentivize this behavior properly, economic incentives need to be strong.
I used the word "politeness" because my coal-age utility (National Grid Massachusetts) doesn't offer time-of-day pricing. They seem to have no interest in doing so beyond occasional small-scale government-funded trials. If they did offer TOD pricing you bet I'd be on it.
But don't underestimate the power of social pressures: "politeness". I don't throw my trash in the next street over, because to do so would be rude. The integrity of the entire Internet depends upon an altruistic TCP endpoint algorithm called "exponential backoff".
California has time of use rates (relatively new and uncommon). And we're beginning to see deep discounts in the middle of the day consistent with the solar. So people may strategically charge during the day. If it's a commuter car on a reasonable commute and you've got 300 miles of range, it's feasible to wait till midday.
There would have to be compensation, of course.