It would depend on the temperature of the water and the exact amount of chlorine, etc. My opinion, by the time you have mixed salt completely it should be gone. Small amounts of water added for top up wouldn't make a difference.
If it makes you feel better go ahead and treat your water. It's probably a good idea, DeChlor and such things are cheap and you never know what the city is going to do. In certain situations they do boost the amount of chlorine they add so better safe than sorry. You can usually predict when they're going to do that and personally I can smell the difference easily so I'll take action when I need to.
There's just no way that this is the reason for your friend's problem though, the chlorine doesn't stick around that long.
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