Can tap water kill aquarium fish if it is not dechlorinated?

It won't kill right away, but after a while, the minerals, phophates, and chloromines are going to build up and it's going contaminate your water, cause an algae bloom, etc. Chloromines unlike chlorine is not a gas and is used by water treatment plants instead of chlorine since chlorine would likely dissipate before it got to the consumer. So your typical decholorinating additive is typically for chloromines. In general, you shouldn't be using tap. I would use reverse osmosis water with additives (depending on fresh vs saltwater) and your tank will be happy.

Chlorine is a gas and evaporates off so it can not build up in aquarium water. All water except distilled and R/O (reverse osmosis filtered) contains other elements that are necessary to sustain life. A build up of salts (increase of GH/KH) etc by evaporation is one of the reasons regular water changes are recommended for most fish and absolutely essential for some Amazon River varieties like Discus.

If you are in an area where the water authorities add chloramine (check with your supplier) then the easiest way is to use a commercially available neutraliser. Only Chlorine is added to my supply and I let it evaporate off for a few hours. I can assure you though that straight R/O water is NOT suitable for supporting aquatic life successfully. In order to make it useable the addition of various trace elements is required and that is a very complicated process to do successfully. I know of one commercial fish breeder in Australia who has a large R/O setup and he 'makes' all his aquarium water. Believe me it is not easy or cheap to do. It will kill eventually! :)