Don't doubt it for a second.
But, tbh, we all knew she was a professional 'celeb' with management when she went in. It's not like Alex being the daughter of the producer or anything... (which she ISN'T before the rumour mill starts
)
Did Faye know? Maybe, but I don't see why BB would edit her guessing correctly before hand if they wanted to keep any kind of conspiracy hidden... nothing we see is by accident after all.