Dumping water from the LFS into your tank will certainly get anything that is in their water into your tank. My way to deal with that is to acclimate the fish then hold a fish net over the sink and pour the fish and water through the net. the wet fish then get put into the receiving tank. My preference is to use a quarantine tank or a tank with no other fish in it. The problem with LFS water is that they run with very high populations and are always on the edge of unhealthy conditions because of it. When you start with water like that and then confine your new fish in a small amount of it for a few hours while acclimating them, the pollutants build to the point that even if I were sure of no disease in the LFS tank water, I still would not want that stuff in my tank.
The water from the LFS will do nothing to help you cycle your tank except to provide some ammonia for your bacteria to eat. The fish they sold you before you should have any will also provide plenty of ammonia so the water is worse than useless. It means you will need to do a water change that much sooner.