Here is the voltage state of charge graph for lead acid thanks to WiKi. Your circuit will work provided you adjust the run out voltage correctly and set the current for one tenth or less of capacity. Check the ICs for heatsink capacity to dissipate the heat generated. I think a simple LED with current limiting resistor can be added between battery positive and the orange link to indicate charge has entered voltage control but this needs checking out as you might find the action is too soft to be meaning full.