Some parts yes, other parts no.
EG: many stretches of the GU allow fishing during the close season because the Law allows it. Some stretches though are licenced to clubs who uphold the close season completely.
To further complicate the issue, there are bits of the canal, around Rickmansworth and Harefield, where the river Colne becomes the canal and on here, the fishing might well be off. Also any site that is an SSSIs (Site of Special Scientific Interest).
Ask around your local tackle shops, tehy should know.