I know I'm late to the party, but some thoughts about this came to my mind just now.
I do believe Fake Geek Girls exist. But: it's not just girls.
Girls are just more obvious, they get more attention. I'm not 100% sure why that is. I think it has to do with gender stereotypes. If a guy says he thinks a woman is sexy, it's like stating that it's going to be a warm sunny day. Everyone can see that, it's not worth mentioning, though nobody minds of you do. But women are supposed not to like sex, so they're not supposed to think of men as sexy, so if they do - they're fan girls. I think this is one aspect, but there's probably more aspects (like men often being able to hide their cluelessness better).
Anyway, so back to Fake Geeks. Yes, I think they exist.
Maybe it's since The Big Bang Theory has become such a big mainstream hit series. Maybe some mainstream celebrity mentioned that they're a "nerd" or "geek" or something. Suddenly being a geek is trendy. Look at all those fake big black glasses.
Take Star Trek for example. Fake geeks would say something like "I'm such a Trekkie, I saw both movies several times." The new movies are Star Trek for non-fans. They took the universe and made it into shiny, sexy action movies. Complete with "inside jokes" to make the fans happy. Looks good, enjoyable for everyone. Now everyone thinks Spock is sexy (not just Jadzia). But they left out some of the things that made Star Trek special - the philosophy, the ethics and morals. Aspects non-fans didn't know existed.
Fake Geeks are annoying.
I know I shouldn't say this. We should be happy that our fandom gets more attention, everyone should be welcome, etc. We should be happy that thanks to Sheldon Cooper more people know what the Doppler effect is. But it's annoying anyway.
I remember when the Lord of the Rings movies were made. You know, the ones by Peter Jackson. I love them, of course. I loved Lord of the Rings way before that. I was a big fan of woodelves and Rangers. My first Pen&Paper roleplaying character was a hunter because it was the closest to a Ranger I could get. My niece - born before the first PJ movie came out - is called Arwen. I knew the Bakshi movie and one of the only two poems I can remember by heart is the Ring poem. Hardly anybody knew what I was talking about - and then suddenly everyone did. Suddenly everyone loved woodelves and Rangers because Legolas was so sexy and Aragorn so cool. It was weird. And it was a little annoying.
It's happened to me again after that. It probably happened to X-Men fans, Sherlock fans, Dr. Who fans and others, too. I loved My Little Pony when I was a kid, but I still don't quite get the fad about them now. It's happening with Big Bang Theory. It will happen again in the future.
So what should we do?
We practice our patience. We're happy about the new fans it will bring to the fandom, the ones that will stick around and be an enrichment to the subculture. And we wait until the others leave again, run to the new fad that's coming up - and we hope they'll do it soon.
And, of course, we'll take all the merchandise we can get...