Not really, or at least not alone. There will always be points at which information must be encrypted. Encryption just pushes the need for the right to be granted to those points. This is not at all a bad idea, of course; just that government recognition of a right to privacy is still important.
If you need to rely on encryption to protect your privacy, then you have very little privacy, because everything that is not encrypted can be snooped on: where you are, who you talk to and about what (because GPG doesn't protect the username and subject), who are your friends (because you can't trust them to encrypt properly).
If you want to escape surveillance, encryption is just one tool. What you really need is good opsec habits. See for examples http://fr.slideshare.net/grugq/opsec-for-hackers