Oh absolutely, I place it within the high possibility of what we’ve seen of Clara so far.
Barring Asylum Of The Daleks (and we’re not even sure if we’re think of Oswin as the same character as Clara, because Jenna mentioned that she’s a totally different character…I’m not sure what that means just yet…) both debut episodes of Clara have featured The Great Intelligence as the villain.
Is it possible Clara was made by the GI as a trap? Yes it’s possible, considering how she was able to stop them by just thinking them obsolete…but how did The Doctor identify that Clara was the key to destroying the Snowmen?
I don’t know…if I didn’t know better, I’d say that we should actually be looking for a connection between The Doctor and The Great Intelligence because of the mention in Hide that: “He has a sliver of ice in his heart.”
Maybe we’re looking in the wrong place. Maybe that’s what is the issue with The Doctor, he’s the one actually being manipulated by The Great Intelligence, following the loss of The Ponds, without even realising it.
It’s another possibility. Perhaps Clara is something else and The Doctor can’t see who she is because of the “ice in his heart”. Perhaps she’s been sent to try to warn The Doctor and make him remember love to destroy the ice in his heart and the Great Intelligence’s hold over him.
Either possibility leads to me honestly believing that the GI is just a front for something else, or connected to something much more dangerous. But there always remains the thought that the GI is much more dangerous than we first thought…especially if it was possible to infiltrate The Doctor.