Fleet Air Arm control could change aircraft supply

Would an independently controlled Fleet Air Arm still have wanted American carrier aircraft?

Yes for expansion and reinforcement, though the need would depend on British output and a naval-controlled service might have developed a wider Commonwealth supply network.

American Corsairs, Avengers, and Wildcats would still have been useful even if the Fleet Air Arm had remained under naval control. Their urgency would have depended on whether British factories were delivering enough suitable carrier aircraft. Direct naval ownership might also have encouraged aircraft-component production in places already supporting the fleet, including Ceylon and Australia. Command arrangements could shape industrial mobilization, though changing control would not automatically produce enough aircraft.