So now that we have Vizago its not only hypothetical anymore:
Can you use Feedback Array while cloaked?
I would say yes. Why? Cause of the blinded pilot ruling, that says you can use FA if blinded:
Cloak rule:
While a ship has a cloak token, it cannot perform attacks.
BP
You cannot perform attacks. After your next opportunity to attack (even if there was no target for an attack), flip this card facedown.