Can you hit a runner with the baseball to get them out?

Yes ... rule 5.10(c)(1) states:

"If an accident to a runner is such as to prevent him from proceeding to a base to which he is entitled, as on a home run hit out of the playing field, or an award of one or more bases, a substitute runner shall be permitted to complete the play."

A situation similar to this occurred in a game between the Boston Red Sox and Toronto Blue Jays in 2005. Gabe Kapler of the Red Sox was on first base when Tony Graffanino hit a home run. Kapler went down with a ruptured achillies tendon between second and third base. Graffanino waited on second base while Kapler was loaded on a cart and taken off the field. Alejandro Machado entered the game as a pinch runner and finished the trot to home plate in Kapler's absence.