It doesn't specifically block phishing sites, but many such sites would also fall under the malicious sites list of the network shield. Many phishing sites would also be using scripting to facilitate driveby downloads, etc. and the web shield and script shield provides protection against that also.
So I do think avast provides protection on phishing sites in general but isn't specifically looking for them.
I use firefox, which also has phishing and malicious site protection, this same protection is available in the major browsers. You can also use OpenDNS as your DNS server and that too has phishing protection. If you use firefox, you can use AdBlockPlus and there are additional filters for phishing sites.
All in all there are more anti-phishing tools than you can shake a stick at, so personally I feel with the avast shields it currently has it doesn't need a specific anti-phishing check.