Running men do get the bonus.
Also see here for full engine/combat workings (including the charge):
https://forums.totalwar.org/vb/showthread.php?t=75233
The charge is affected by charging unit cohesion, melee mode setting, as well as front men touching the enemy and enemy front touched.
For exaple if your cavalry is charging after running some distance put "hold formation" while running and release it to "engage at will" shortly before they touch the opponents.(The more the better applies).
Many Thanks
Noir
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