Ballsy to do that in the middle of an urban environment.
That could be a new market for all the junkyards

but you can get some unwanted effects with playing with the soil chemistry.
The soil is very good at buffering its PH, so it needs an huge amount of added substances to be effective. The PH rules the availability of the elements for the plants. It may be good for the plants, or not, but it affects physically the behavior of the soil too. The calcium binds with the minerals of the clay, brakes the compactness and makes the soil more granular, which is good for both the drainage and the atmospheric exchanges. The roots prefer that by a long shot. Take out the calcium, the clay returns to its compact state, the soil becomes impermeable and asphyxiating. Most of the plants wouldn't take the prank very well.
Beside, calcium carbonate (limestone) and sulfuric acid makes CO² and gypsum. The last one is more soluble than the limestone and is washed away quicker. The soil is depleted and the water loaded with the gypsum is deemed undrinkable.
I forgot one problem. The sulfuric acid in the batteries is heavily contaminated by lead. Many ones would object to dump it the environment.