Sewage and water bills normally go hand in hand. Most places only have meters on the water so the more water you use, the more sewage you create. (in theory) So, in places that have city water and sewer, if you water your lawn, the sewage bill will be higher, but if you let a truck dump 1000 gallons of water into your toilet, your sewage bill won't go up at all.
So, in most locations, no! It will not raise your bill.