Question:

When using cold water only, do I really involve tankless water heater into operation?

Answer:

It depends on the faucet you use. If you use cold faucet, your water heater remains uninvolved. But if you use hot water faucet, it is inevitable that you water heater starts to operate. Using hot water just for a few seconds releases certain amount of hot water and makes the water heater to heat fresh cold water.