Lots of people are wrong. The stuff in Nair attacks sulfur bridges in keratine. This makes it physically fragile so you can scrape it off.
It doesn’t dissolve the keratin though.
In theory you could break it into lots of small pieces by say pointing a water jet down the drain (or plunging or whatever) after treatment. Whether this is enough to loosen it will have a lot to do with other stuff in the drain/geometry/penetration depth. It may just make a gel that plugs the drain.