This would indeed work. MWG could be setup in some transparent mode (router, wccp, layer 2). The traffic would then be redirected to MWG and it would filter it like you do any other traffic.
As far as non-HTTP traffic like DNS, that traffic could just pass through MWG on the way to it's original destination (like the DNS server).
This is pretty common to have MWG setup in transparent router mode, then setting it as a default gateway (in some way shape or form).