Is water on the outside of an electric kettle dangerous?
Kettles often drip a bit when they pour, and that runs down the outside. So a kettle has to be designed for a little water on the outside (though clearly not for a complete soaking).

If you have a shiny kettle and like to keep it that way, limescale will be increased by getting it wet more often, but that's the only real harm, and anyway is easily fixed. 

I prefer to turn the tap off before removing the kettle though, because it's convenient the way my kitchen is laid out. Otherwise I get a bit of splashing near the sink that I might not want.