leaving it on and dry for 3 days will usually not start a fire but the potential is still there. What usually starts the fire is the plastic of the coffe maker melting and then getting on the burner element. With the pot left on a burner it acts as a heat wick and can allow enough heat to be nearer to the plastic componants than usual. This is where the fire starts.
Extensive testing on coffee makers is done at the ansi labs as well as independant consumer protection labs. These tests are usually pretty thourough. and Im sure include a dry pot on the burner test.
If what you seek is an absolute yes or no answer to your fire question.........................Well that you will have to ask fate itself. There are just too many "ifs" that go with that answer.