Can you put instant coffee in a coffee maker?

It is a bad idea. Hot water, straight from the faucet, contains more dissolved minerals (calcium, assorted salts, etc) than cold water does. It's simply because of the temperature...more solids can be dissolved in hot water than in cold.

The same minerals that cause the scaling and "hard water" deposits in your bathtub will also clog up your Mr. Coffee. There are coffee machine cleaners (chemicals) that help remove these deposits, but eventually they'll build up so badly that the machine is ruined. Using hot water, rather than cold, will ultimately shorten the life of your coffee maker.