They can help by improving the financial viability of intermittent power sources like wind by acting as soak for excess production. This allows you to invest greater amounts in wind farms and hence reduce overall coal use.
It is possible that doing this might have the opposite effect if the wind farms are making most of their profit from the price spikes. In this case putting power back into the system by lowering usage in peak times might make wind less financially viable.
The price spikes exist regardless, because those are from high-usage hours (basically day hours) and at a longer range, at summers and winters (depending on where you are) because of heating and a/c.
A lot of factories already use more energy in the evening/mornings, because electricity is cheaper at those times.
Storage technologies are a huge potential to be explored.
It is possible that doing this might have the opposite effect if the wind farms are making most of their profit from the price spikes. In this case putting power back into the system by lowering usage in peak times might make wind less financially viable.