I don't see rules prohibiting the use of Action Cards by captured leaders. Here's the scenario that raised the question:
Luke Skywalker & Dodonna were on the 'Plan the Assault' mission card, and flew to the Death Star system (Geonosis). The assault failed, with the Rebel fighters were all wiped out by the end of Round 1.
The Empire sent Vader and Gen Veers on the 'Capture Rebel Operative' mission. The attempt succeeded. On a subsequent turn, the Empire used Boba Fett in Geonosis for the 'Carbon Freeze' mission on captured Luke.
The Rebellion had 1 leader remaining in the Leader Pool and sent had Leia take the remainder of the Rebel fleet from Ryloth to Geonosis. The TIEs were depleted from the earlier raid, so at the end of Round 1, there were 2 X-Wings remaining.
So the question came up, 'Can I play the One in a Million action card?' Luke was in the system of the battle, but captured in carbonite. But, I don't see a rule that prohibits the play of action cards, just the requirement that the leader is in the same system. Thematically, perhaps he was in a Force trance in the carbonite, directing the pilots to the exhaust ports.
As it turns out, the pilots got a burst result on the first round, so I didn't have to play the card. But, we still have the question.
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In the Rule Reference and in the Learn to play... it does not get mentioned. Altough it feels incorrect, it does not state it.
The FAQ AND ERRATA of may 18, 2016 does.
On page 2.
"Q: Can a captured leader use action cards?