Can units join a character in combat?
From BRB p97.

A character must move into a unit to join it.  There is no rule that allows the unit to move to the character.

A character cannot join a unit in close combat.

You can however, simply charge into combat alongside the character.  This is often to your advantage for that particular combat, other than not being able to use the character's leadership.  (Two chances to catch the enemy if they flee, if one or the other of yours flees, the other may hold and prevent them form being run down, etc.)