I believe the correct English translation should be "Does such a man exist? / Does a man like that exist?"
I don't think it's (officially) wrong, but it's definitely not the most common way of asking the question.
I'd say this phrasing would most likely be used to express surprise. Like... "I want to marry a guy who's tall, handsome, smart, really, really rich, very sensitive and caring, doesn't have any bad habits, isn't nuts or a jerk, and wouldn't think it's weird that I want to move to Mars." "Such a man EXISTS?!?!"
See 2200Lucia60's comment above for more standard translations.