I believe part of an artists success is based on trends, but generally artists influence each other and they create works that are favored by the public by drawing on various sources. I believe Salvador Dali's pieces are very timeless so I am sure he could have made it in today's cynical culture.
I believe they would be able to succeed in our culture because they are painters and most painters are open and accepting to the way things are and if they have been surrounded by the event that we have endured they would probably have an opinion towards it as well. Painters don't stop painting good pictures because the culture changed.
Many painters could survive from back them in this time. The world has always been cynical, but just a little more so now. It would be no problem for them to handle today's world. There are a few though who would not be able to handle it. One probably being Leonardo Da vinci.
I think that in current times we have a cynical culture, but we have such a diverse group of people that enjoy many different types of work. I think that painters like Salvador Dali would be capable of succeeding because of the diversity of interests of other people. He is also very talented and that talent would rise above.
I think that painters like Salvador Dali are a product of consumerism in their era. And that means no, I don't think they'd meet with great success in the current culture, cynical as it is. Tastes have changed. While we revere Dali for his works, any new artist trying that technique for the first time would be relegated to showing his work on a blog.