Yes, and plenty of companies are doing just that. The effect is that as they charge the batteries, they increase demand and that increases the electricity price a bit. Grid doesn't tip over and everybody wins!

Trouble is that at some point they run out of batteries. Batteries are expensive. And when they run out of batteries, the demand drops and the grid has to figure out where to dump the excess. And the price drops again.

Pumped hydro is a more scalable solution, but it's slow to react and even that has its limits.