Open-cell foam: yes, significantly. Closed-cell foam: moderate. For dedicated sound dampening (theater rooms, offices), open-cell or specialty acoustic foam. Closed-cell prioritizes thermal/vapor performance.
More detail
Sound transmission reduction is measured in STC (sound transmission class). Open-cell foam in a 2x4 wall cavity adds approximately STC 5-7 to the assembly versus an empty cavity, which is a perceptible improvement (cuts perceived loudness by roughly 25%). Closed-cell foam in the same cavity adds STC 2-4 because the denser foam is acoustically more reflective. For dedicated acoustic applications (home theater, recording studio, home office where outside noise needs to be controlled), the right approach is acoustic-rated drywall (5/8" Type X with mass-loaded vinyl backing) plus open-cell foam in the cavity. For typical Cincinnati residential where sound dampening is a secondary benefit alongside thermal performance, open-cell foam in interior walls between bedrooms is a low-cost upgrade. Closed-cell on exterior walls and below-grade prioritizes thermal and vapor properties; the modest sound benefit is incidental. Cincinnati home-office-and-theater context: as more homeowners convert basements and bonus rooms to home offices and entertainment spaces, sound dampening has become a more frequent foam-project objective. Open-cell foam in interior walls between bedrooms and a basement home office cuts perceived loudness substantially at modest incremental cost. Our Cincinnati installers can spec acoustic-targeted assemblies as part of broader foam projects.