Yes, it does! It is an analytical skill that involves the interpretation of symbols and the completion of puzzles. There are programs to help with solving crosswords, so there are also resources for beginning programmers which teach them how to solve their first programming puzzle. Programming languages have many similarities, including syntax. If you love doing crosswords then you may just enjoy learning about programming as well.
The short answer is yes! Of course, not all computer programmers come from a crossword-solving background but it's true that the two types of activities have many similarities in terms of logic and notation plus there are programs that can be used to help beginners who need assistance with their first "puzzle." One similarity between the fields is syntax...