After adding 1mL of saturated NaNO3 solution to 3mL of saturated NaCl solution, no NaCl is precipitated. Why is this?

I thought that nitrate would not be involved at all, and increasing the concentration of Na+ should push the reaction towards solid NaCl. But then I considered that adding the second solution causes the concentration of chloride ions to decrease. If it decreased enough, that could counterbalance the increase in sodium ions and preserve equilibrium without the reaction shifting. Is this a correct line of thinking?

Question

After adding 1mL of saturated NaNO3 solution to 3mL of saturated NaCl solution, no NaCl is precipitated.  Why is this?

I thought that nitrate would not be involved at all, and increasing the concentration of Na+ should push the reaction towards solid NaCl.  But then I considered that adding the second solution causes the concentration of chloride ions to decrease.  If it decreased enough, that could counterbalance the increase in sodium ions and preserve equilibrium without the reaction shifting.  Is this a correct line of thinking?