I beg to differ. I fish Cold Brook (aka 'Keuka Inlet') at the southern end of Keuka lake in the spring and there are a number of large carp there, at least in the public sections south of the 54A bridge. They may not be there year-round, but I know for sure they are there in full force during the spring, churning up the water, creating huge swirls and waves whenever they're spooked, and breaking even 9+ lb line/leaders. They look to be in the 20-30 lb range. This part of the stream is public land and the carp could be legal for bow-fishing if there weren't houses within the 500 feet minimum. They'd be easy targets in slow moving water.
I have seen and caught the suckers you're referring too- entirely different fish, obviously smaller and slimmer than carp, and they face upstream in the fast moving shallows, usually in tight groups of 2-3. They are the ones I always see in Catherine Creek that are practically catch-able with bare hands. In the past couple years I've been to the Cohocton river, Owasco inlet, Butternut Creek, Mill Creek, Neil Creek, Cayuga Inlet, Catherine Creek and Naples Creek and can tell the difference between a sucker and a carp. Check out Cold Brook for yourself, the carp there are impossible to miss.