No. Web Shield serves a different purpose. While Network Shield is checking malicious packets (like Sasser or MSBlast generated TCP traffic) and checking of webpage addresses, Web Shield is scanning the actual transfered data. So anytime you view a webpage, pretty much entire content of that webpage is scanned by avast! even before it actually enters the browsers and also all downloaded files that come through HTTP protocol are also scanned. This way you can prevent known exploits from affecting possibly still vulnerable browser.
It also prevents known bad downloads (files) from even reaching your hard drive.
Thats why it's almost critical to run at least Standard Shield, Network Shield and Web Shield providers together (not just one or another alone), because only together they fully cover wider range of possible security holes to your system and provide maximum security.
All other providers are not exactly necessary but they also provide additional protection layer depending on what programs you are using (email clients, P2P software, IM etc).