No. This is a persistent urban myth.
Birmingham's total historic canal mileage (including suburban/Black Country network) exceeds Venice's city-center length — but Venice's canals are its streets; Birmingham's were freight arteries. Different functions, scales, and urban forms.
Birmingham proudly markets its "more canals than Venice" claim for tourism — but it's a comparison of total historic network length vs. active urban canals, not a like-for-like measure.