My last round as the Union against Athena I played with that option. Interestingly enough, sometimes I was allowed to move not activated leaders, so it is not as strict as the tooltip implies. And no, it seems not to affect units with no leader. But you can't take e.g. a division from a locked Corps because the divisional leader might be active.
Regarding the game, i guess it slowed me down a little bit (victory in April '64, taking Richmond and general collapse of the southern defense in the west), but I don't think it is as hard a constraint as one might think.
It can become a serious problem for deep raids, especially in autumn - I lost a couple of (mainly cavalry) divisions that way (though I can't just blame the activation for those losses :bonk
Otherwise I fought with the original army leaders, McDowell and Banks in the east, McClellan, Fremont and Rosecrans west and Butler around New Orleans. Grant took over in '63 from Fremont when he went for little Macs command as the latter decided to run for presidency. So I was often enough already hampered enough by my commanders anyway...