The use of blank cartridges, ammunition with explosive powder but without a projectile, pre-dates the movies, so it is entirely possible, and very likely. In fact, it's difficult to imagine any other technique or device that could have been used at the time.
An invention that would not be used in movies until decades later is the squib, a small explosive device used to simulate the impact of a bullet. In early films, a bullet impact on the human body was merely pantomimed, but bullet hits on other objects were often accomplished using live ammunition. Blank cartridges were difficult to obtain and relatively expensive, so guns on sets often fired live rounds. James Cagney famously refused to allow live ammo to be fired in his direction when he was almost hit on the set of "Taxi" (1932). In "The Public Enemy," released a year earlier, Cagney ducks around the corner of a building. The stonework is then riddled and powdered by bullets, real bullets fired by a marksman off screen.
Eventually, squibs and other explosive devices would be used to suggest the effect of a bullet's impact. Some sources date the first uses of squibs in movies to the 1950's, specifically to squibs combined with blood packets for wounding impacts, but explosives for bullet hits on set pieces were probably employed much earlier.
Blank cartridges and squibs are not used without risk. No matter how small, a squib is still an explosive device, and should be handled and deployed only by licensed effects technicians. I was present on a set when a foolhardy effects technician, who was not sufficiently stocked with squibs for a day's shoot, lost a finger while trying to cut some of his squibs in half. And blank cartridges have been responsible for at least two deaths, the most famous being Brandon Lee during the filming of "The Crow." The circumstances leading to Lee's death were tragic and coincidental, requiring a complex combination of mistakes, misadventure, providence and happenstance.
The death of actor Jon-Erik Hexum was the result of foolishness, complacency, and a lack of knowledge and respect for the technology. He used a gun loaded with blanks as if it were a toy and played a fatal game of Russian Roulette, reportedly to ease the tension on the set. Michael Mann opted to use live ammunition to shatter a real glass structure during a climactic scene in "Manhunter." Injuries were just barely averted, although actor William Petersen was seriously injured by the subsequently broken glass. My good friend, make-up artist Jeff Goodwin, devised a method of producing blood hits using compressed air to avoid the use of explosives when safety conscious special effects technicians fled the set and never returned. The results can be seen here, starting at about 7 minutes in.
Jeff would later be tasked by director Mann to design a technique that would accomplish bullet hits on mostly naked stunt performers for "Last of the Mohicans." Jeff discusses "Mohicans" and squibs about 1:50 into this clip.
In conclusion, here's Martin Scorsese's homage to "The Great Train Robbery" from "Goodfellas," as suggested by one of my wonderful students.