The difference between a randoneur and a "real" touring bike is generally very slight. Touring bikes tend to have heavier tubing and hence have a great deal harsher ride when they aren't loaded. There may also be a difference in wheelbase length that isn't very important.
But "great deal harsher" may not even be noticeable to most people.
So your answer is - get a good modern touring bike and you won't have any problems using it for randoneuring.