Your serial number puts the ship date around 1920. That does make your gun a modern firearm by the BATF rules and regulations.
Most people don't realize that almost every model that S&W introduced started with a new set of serial numbers. The 32 Double Action ran to serial number 327,641 and the Safety Hammerless revolvers ran into the 200,000 serial number range, so both models had a 221,273 serial number. All other early 32 caliber models, like the Model 1 1/2 & Model 2 tip-ups, to the 32 Single Action revolvers ended well before a quarter million were made.