No, it is not always safe to pour waste chemicals and solution down the sink with lots of water because it could be harmful to the environment. When you pour materials down the drain they either enter a septic system or a municipal sewer system. If the material enter a septic system, it goes into a tank buried underground where the solids settle and decompose. The rest of the wastewater is than released into a drain field where it goes into the soil. Sometimes the wastewater kills the good bacteria and can contaminate ground water or surface water.
A municipal sewer system the wastewater goes to a central sewage plant, where after treatment, it is then released into lakes, rivers and streams. Some hazardous household waste can pass through the system unchanged and pollute the waters. Also the wastewater may affect the plumbing or collect in the trap and release fumes through the drains. Most sewage facilities aren’t capable of removing such toxic substances.
So, No, it is not always safe to pour chemicals and solutions down the sink even with a lot of water.