Does addition of distilled water to an acid-base titration affect the end-result?
It affects the concentration of the acid; it does not affect the number of moles of acid or number of moles of sodium carbonate.
I presume you are titrating a known mass of sodium carbonate with sulfuric acid, and we represent the equation by:
Sodium carbonate thus reacts 1:1 with sulfuric acid.
When you do a titration, you are titrating to an endpoint. You can use water to rinse the side of the flask, so all the reagents are in the reaction flask. So the presence of water should not affect the endpoint.