VF-12 completed carrier qual by April of 1943.
Starting May 1, 1943, VF-17 landed F4U-1's and eventually all pilots got their five traps. VF-17 deployed aboard Bunker Hill with new F4U-1A's from the factory September 10 of '43.
So, VF-12 and VF-17 successfully completed carrier qual with F4U-1's.
Here's one opinion on why they did not remain as carrier squadrons:
"The trip to the West Coast was uneventful, and they sortied from San Diego on September 28.
But a few days out, official lightning struck. VF-17 was detached from Bunker Hill, and ordered to the island of Espiritu Santo, to operate as a land-based squadron. The problem was one of logistics, not of operations. The high command knew that Blackburn's Corsairs could operate from a carrier. But as the only Corsair squadron in a Navy full of Grumman Hellcats and Wildcats, supplying and maintaining them would be a headache."
Short answer: Yes, they can operate from carriers.