Marx certainly did not believe that "the evil capiralism would provide the means to get there". I would assert that he believed that capitalism held the seeds of its own destruction within it.
He believed it would indeed do everything in its power to survive, including eviscerating and overturning any democractic process that might result ultimately in the loss of its own power, even if those were democratic processess that it had created, especially one where people "chose" socialism.