No, you can’t do that. It is not even possible under the rules of common sense. The national building codes of the US and Canada will surely be against it.
Even the local plumbing ordinances you have. Your sink will need to be connected to the sanitary sewer. The floor drain will stay connected to the storm sewer.
If you are in a more seasoned home, where they are shared, you could do it. However, you should uncover the floor and make the association sub-section with inflexible associations and not adaptable hose or line.
You could wind up having a flood in the cellar and having sewage, storm water, or both coming into the basement. But not having an exit plan on the off chance that you don’t do it appropriately.