No, no.
Even when you dump clean water down the sewer, it has to be treated. First, to make it clean water fit to come out of your tap. Then to clean it up again before it is dumped.
When you dilute the filth in the sewage system, it may lead to cleaner, i.e. less concentrated, sewage, but still and also increase the volume of it, increase the volume that has to be treated.

So another conclusion we can safely draw is that the more water you use, the more water will be treated.
At a price. Which counts as environmental costs.