If the firecracker was homemade, from gunpowder, it would.
AI talk:
Yes, firecrackers smell different than gunsmoke. While both contain sulfur compounds, firecrackers use traditional black powder, giving off a strong "rotten egg" and charcoal smell. Modern firearms use relatively smokeless powder, which leaves behind a sharper, chemical, or "match-like" smell.
Firecrackers generally do not have cordite in the powder, while gunpowder does.