While I can't speak for reality, I would say... Some people in japan definitely think so.
Why do I say this?
Because 'otaku girls' show up in anime series sometimes, (and are referred to as such).
Case in point, Ouron high school host club.
Renge Houshakuji - is described as an otaku by Kyoya not too long after first showing up.
I've seen similar characters either being referred to as Otaku, or calling themselves that in other series as well.
(another candidate that comes to mind, though I don't recall if anyone in the series called her an otaku. - they did call her a a hikikomori though is Kona Furugoori from robotics;notes)
(one of the maIn characters from bamboo blade also comes to mind)
In any event, while that's fiction, the existence of fictional examples imply the existence of the real thing as well.
Though, of course, the Japanese understanding of what an otaku is, compared to the western idea of it don't nessesarily match either.
Then there's the whole thing which still seems to persist that 'nerd/geek girls' are incredibly rare in general...
Which then rather counterintuitively led to the idea that we don't exist at all, and surely, therefore anyone that seems to be one is faking it for some... Reason. >_>
All I know is, we exist. Wether anyone would call us an otaku or geek or nerd or whatever to our face, I'm not really sure.
Especially if it isn't immediately obvious from the kind of clothes you're wearing, or anything else about you... Why would it even occur to anyone?
Anyway... I think they definitely exist in fiction. And I know they exist in reality. (even if people don't always openly refer to them as such)
I can definitely compile a long list of fictional female characters that meet the criteria. It's more of a challenge finding ones explicitly being described as Otaku though.