Once a solution is saturated with a solute (aqueous NaCl in this case), the solution's freezing point will stabilize. Additional solute cannot dissolve into a saturated solution, so there can be no further molecular-level interference of solute molecules with solvent (water) crystallization.

However, if enough salt crystals are added to the saturated solution to form a slurry, I believe freezing point may be further depressed by macrodilution of water to the point that it can't freeze. I'm not positive about this latter contention. A physical chemist will know better.