You need to post much more info. The link below will tell you what info.
Yes the correct volume of chlorine combined with the proper size retention (tank or tanks etc.) to get the correct length of contact time will treat the iron and manganese so the softener doesn't have to deal with them. The chlorine will create oxidation 'sediment' (rust etc.) that will have to be filtered out before the softener. If you have the right filter size now, you may be able to use it.
You may be able to insert the softener into the present system after the carbon filter. You need to tell us what size filter and what brand and model control valve. Are the f.loc tanks open air (depressurized) or closed (pressurized)?