And voters can't sweep a 'Marxist' leader from power, because they don't have elections.

Some do, some don't, the same as applies with people who adhere to other economic theories.

The fact that Hitler was a vegetarian doesn't mean that vegetarianism is intrinsically undemocratic. In the same way the fact that Stalin and Co claimed to be Marxists doesn't mean that Marxism is intrinsically undemocratic. For that matter, the fact that Pinochet was a devotee of a form of Capitalism doesn't mean that all Capitalists are Pinochets.