Having just come off Otumba and Pavia I can say that single clicking on a unit does make them charge cohesively, AND they can even do it to moving enemy units. Really Nasty. (This is in the second Demo BTW, the full game may vary).

For reference in Otumba I had the enemy peasants start running at 90 degrees to my 2 full units of conquistadors, they STILL pulled of a frightening charge in spite of this that killed over 150 peasants from 2 units.

Likewise similar charges into other units seemed to produce similar effects (a rear charge at a bodyguard unit killed all but 2 guys, one being the general).