No. As long as people keep using the same online communications to plan inflicting harm on society as society does to exchange pictures of grandkids and recipes, those communications will keep being monitored, and thus we can have no expectation of privacy. Liberties have always been compromised for the sake of security, Benjamin Frankliin quotes notwithstanding.
But! Taking these numbers at face value, the low error rate tells us that, yes, we can have privacy with pretty high probability. As with all things in life, it is not guaranteed, but these are much better chances than what we can expect in other aspects of life. I mean, tens of thousands erroneously picked up over many months out of the billions of emails exchanged daily? Why, you're more likely to die in a terrorist attack than be snooped on [1]!
[1] No, I haven't run the numbers, just saying so for dramatic effect :-P
