What happens when a popular manga becomes a late night anime?

“If it’s late at night then it’s geared towards otaku” is an argument that gets tossed around fairly often, even by myself.

But then there are examples of anime adapted from popular manga that end up showing at midnight or later. Nana, the most popular shoujo manga around, had an anime adaptation with an 11:30pm time slot. Glass Mask, one of the most popular shoujo manga of all time, aired at 2:00am with its 2005 remake. In the case of Glass Mask, the fact that it is not hip and modern (though the manga is still running!) may have contributed to this late-night airing but I still do find it unusual.

Assuming that late-night really DOES equal otaku, is it possible for a manga with general popularity to be turned into an otaku-targeted anime?
However, if we were to assume that late-night DOES NOT necessarily mean the show is meant for otaku, just how difficult is it to get a decent time slot on the Japanese air waves?

Finally, are there any examples of otaku-oriented manga becoming popular anime?