If they can pass the necessary ship driving exams and put the years in then why not?
Navaleye, weren't CVs always captained by one of the gold wings brigade to prevent 'the old navy' taking over and reinstating plodder thinking? I'm fairly certain this still pertains with the CVNs. Do they have to pass the ship driving test? (brings back memories of the Navy Lark, "Left hand down a bit, Chief!")