A good question by the OP as my electric kettle is suffering from a build up of limescale. Vinegar used to be a common method of curing the problem in the UK before they brought out the fancy product used today.
I'm sure you could use it but you would obviously have to put several flushings of cold water through the machine before use or as Gaucho100K says you may end up with odd tasting coffee. Right enough, I've been having odd tasting coffee at home since I arrived here.

I would certainly be interested to know as well where the product can be bought and we can then leave the vinegar for the salad. ^