Pretty much straight away actually.

In Australia prices were reduced by over $50 a year per person in the state on average once a similar battery went online. Similar policies and market there to this case too. Details: https://en.m.wikipedia.org/wiki/Hornsdale_Power_Reserve

I get that it's easy to be pessimistic but batteries like the above not only pay themselves off in 2years (From the article above, $46million profit in one year alone on a $90million install cost!) they also cut prices on the grid from day one.

Behind the scenes prices can fluctuate between <0 and >100x baseline. These types of installations immediately smooth out the costs. As long as you have competing wholesalers/providers the price reductions will come through pretty quickly based on similar cases.