Does Government Spying Threaten Privilege?

A recent report shows that US government spying has gone even farther beyond what Edward Snowden disclosed. The National Security Agency has apparently broken the security of two major in-the-cloud email systems, Gmail and Yahoo! mail. The story reports that the spy agency intercepted metadata and content of over 180,000,000 emails in the space of a month.

Does knowledge of this activity mean that a lawyer who uses one of these services for business email waives privilege in the content? Is it like speaking to your client in a criminal matter with a police officer clearly within earshot?

Or does the sheer bulk of the interception provide enough privacy by obscurity to protect privilege? Does it matter if the lawyer is transmitting information about a dispute with government? Is the NSA (or CSEC in Canada) going to be analysing the data for anything but evidence of terrorism e.g. links or connections with suspected people? (Not that that is necessarily a good thing, or effective, or justifiable – just asking about the impact on privilege, here.)

Given the decryption capacities of the major spy agencies, would it make a difference to the assertion of privilege that one had encrypted one’s webmail with some off-the-shelf or comes-with-the-software encryption service?

I am inclined to think that if knowledge of this activity means privilege is waived, then there will be no more privilege, since the security agencies seem to be looking at everything . . .