Sort of, but not really. The water on the input side of your tap is much more valuable than the sewer side.
It's not usable for drinking water, it is usable for greywater purposes. If you've got a septic system, it'll go through that into the local ground water, if not, it'll go into the septic sewer and eventually to a treatment plant, and from there a river.
If it was originally aquifer water, you've taken (likely) high quality water from a diminishing resource and put it in the environment.
We still get yellowpages telephone books vomited on our porch to throw away, about twice a year. Three guys in an overloaded car grace us with them, one guy on each side of the street, throwing yellowpages at houses, and one guy driving.
All paper recycling does is keep paper prices low enough that these people can afford to print these things and force them on every household in a city. Remind me why I should be recycling a renewable resource again? You end up subsidizing marginal paper using businesses, who enjoy cheaper paper prices because of the efforts of millions of people, all because society thinks tree farmers should be paid less.
It is not like drywall manufacturing, where the water is tainted and should not be put back into the supply.