There is no relation whatsoever to the root/spice of the same name.
The term originates in American television, specifically Gilligan’s Island. In the show there were two single attractive females: “Mary Ann” (a brunette), and “Ginger” (a pale redhead). There was much debate among viewers as to who was the more attractive of the two. Eventually the debates devolved to a simple personal preference: Mary Ann or Ginger? Basically were brunettes or redheads more attractive?
As this was a very popular show at the time of its airing, the debate became a widespread phenomenon. As with most popular trends they take a while to traverse the pond. Syndication of the show and its popularity in America led to eventual reruns broadcast in the U.K.
If you need any evidence simply look up Gilligan’s Island or actress Tina Louise who played Ginger on the show. As brunettes are more plentiful and are considered less exotic, the term Mary Ann never caught on as a generalization for them.
References: I grew up in the States and was around for the discussions/debates.
I will attempt to track down a reference. However, I expect that resources will be scarce at best. As with most trends and slang terms there is no immediate empirical evidence available. Rather, data must be extrapolated from the phenomenon in order to explain it. This is one reason why currently popular terms are not constantly added to dictionaries.
I agree that the character’s name is likely derived from the scarcely used and defunct term. But the 19th century definition is not directly responsible for the current popularity of the term. Most linguistic trends in this day and age are not rooted in origins and dictionary history but rather in popular media. If Jeremy Clarkson, Matt Smith, Snooky, Paris Hilton or simply a cleverly named fictional character present a “new” idea or catch phrase and the public latches onto the term and regurgitates it, the original etymology of the word is not the current source of the term’s popularity.
If someone uses the term based solely upon the character, be it of their own “creation” or via the socially accepted practice of doing so, there is no direct connection to the traditional term.