Strictly speaking, no. Volition confirmed pre-launch that is 100% cosmetic. However, the perception of gameplay changes drastically.
Shaping Steelport: A Comprehensive Guide to Body Mods in Saints Row (2022) saints row 2022 body mod
The official customization system offers granular control over your character's physical presence without needing external software: Strictly speaking, no
Exaggerated body proportions will often "poke through" clothing items. saints row 2022 body mod