I read Contact many years ago (I haven't seen the Jodie Foster movie). I have some measure of respect for Sagan as an astronomer, and his Cosmos television shows inspired me to study science when I was a child. That idea from Contact makes great fiction.
Yeah. It's my standard answer when somebody asks what I'd consider to be proof of God's existence. (It's actually an interesting philosophical question, *could* God specify the value of pi if he wanted to? It can be derived directly from the integers, so maybe not. He might have to use more "arbitrary" values, like the ratio of proton and electron masses. But I digress.) You're right though; if God is hiding his presence from us for some reason, we'll find out when he wants us to and not before.
The book (and derivatively, the movie) "Contact" was a cheap ripoff of an earlier book (serialized in Analog?) called "The Siren Stars."