Seems like every site I have found indicates the suppressor being added post WWII.
Evaluation of the M3/M3A1 for issue to the PN/PMC by N-11 also revealed the weapon's adaptability to Philippine Marine Corps Battallion Special Operations Platoon requirement for a silenced, cost-effective weapon. A prototype was built with a locally developed silencer and test-fired at Fort Bonifacio Naval Station in May, 2004.
In the video clip 5 pepper poppers (1/3 the size of a human target) were engaged at 40 meters and all targets were down in 3.5 seconds with 25 rounds expended.
Submachine gun silencers typically reduce sound by around 30-40 decibels but the silenced M3 has an advantage over silenced 9mm submachine guns currently in use since the .45 bullet travels at subsonic speed (less than 1000 fps) and does not produce an audible "crack" like a standard 9mm Parabellum round (around 1250 fps) as it breaks the sound barrier. Silenced weapons such as the British L34 Sterling used by PN-SWAG units require special subsonic rounds for more effective sound suppression.
http://www.timawa.net/m3/m3.htm