No with a reasonably large grid you only need to overprovison no need for battery.

But this is really a question of economics, the mix of how much storage you want to include is really a question of cost and the specific grid. One should also say that pretty much every grid already has some level of overprovisioning, because otherwise you run into problems when some exceptional events hit.

In the end why would you pay for more expensive nuclear if you can get more capacity for the same price with wind/solar. So it is cheaper to build the overprovisioning with that. Moreover if the current trends for storage prices continue then things become cheaper still.