I don't know. I first heard of the 'Turing Test' at school, long before I knew about his conviction. And his work during WWII gives him a bit of a hero status, even for people who aren't interested in computers.
This is a common pattern, journalists propagate the scientific tales of scientists they like for non-scientific reasons. I wonder why the name "Einstein" is synonymous with "genius" in the media while Maxwell, von Neumann, Godel, Newton and many others could equally fit. I suspect Einstein has been so favored by the media to the exclusion of others because Einstein was a major proponent of Zionism. Similarly people call modern computers "Turing Machines" even though they are more accurately "von Neumann machines" because journalists love that after they've revered Turing as the mega-genius-man of computers, they can turn around and treat computers as a cause celebre of gay pride.