You probable could drive after a local but I would advise against it. My nose was done with local but they knocked me out while they numbed me. Should the decision be made for a VFS, you will be knocked out and may need a hospital stay if you are unable to go home. It's also possible with the stress of the surgery, it may not be wise to drive for a while after surgery. I think a cab or UBER would be a wise decision.
As for CTA, I have heard of a few failures as the result of the tie failing but otherwise the surgery seems to be reliable. It's more difficult learning to speak after CTA than VFS and i preferred not to have it because it limits your range. I may never sing but I wanted to leave my options open.