Tea kettles are a great way to add humidity to a room or a house for that matter.
As far as I am concerned they are way better than humidifiers. They do not require any extra energy, and they do not have any filters to clean. Besides they add to the ambiance.
We use one all the time. Oh! one caution; don't let them run out of water as that can burn out the bottom of the kettle.

yes it would in effect work the same, one thing though, don't let the pot run out, you'll get deposits from the water in it as you evaporate out the water, and when you let it run dry, it can generate some smoke and a terrible stench.

this works great! They even make iron kettles for this specific reason. It will definitly help moisturize your air. Plus cheaper than running a humidifier.

When my parents had a wood burning stove, they kept a large pot full of water on the stove - it seemed to work great - we never really needed a humidifier - except when we got sick - then they switched to an oil furnance and always need to run a humidifier in the winter months - I would say the kettles or a pot full of water would be comprable

Sure it will. I used to get good results by placing a pan of water on top of the radiator. Might as well use these methods instead of buying and running a humidifier.

sure it will. you can add a scent to the water and the house will smell good too.