Yes, mostly through localised concentration and low pH. Here is how to dose so you protect the surface as well as the water.
Granular shock can bleach acrylic, etch headrests, and damage vinyl liners if it is added wrong. The damage is almost always avoidable. Two rules cover most of it: pre-dissolve before adding, and balance pH first.
Granular chlorine added neat to a tub floor concentrates locally to several hundred ppm before the jets disperse it. At that concentration it bleaches almost any colour and softens vinyl.
Low-pH water amplifies the damage. Shocking at pH 7.0 is much harsher than the same shock at pH 7.4, because the active hypochlorous acid form is more aggressive at low pH.
The damage looks like white patches, faded headrests, or, in vinyl liners, soft spots that develop into pinholes.
Always pre-dissolve granular shock in a bucket of tub water (about a litre per 100g of granules). Pour the dissolved solution into the tub with the jets running.
Never throw granules onto the water surface. They sink in clumps and concentrate on whatever is below.
Check pH first. If it is below 7.2, add alkalinity increaser and wait an hour before shocking. If it is above 7.8, add pH down and wait. Shock at pH 7.4 to 7.6 for the gentlest effect.
Wipe the waterline with a soft cloth weekly. Body oils and shock residues build up at the line and can stain the acrylic permanently if left.
Do not use scouring pads on acrylic. Microfibre or a soft cloth only.
Replace headrests every two to three years. Even with perfect care, the constant cycling of warm water and oxidiser softens them over time. They are inexpensive parts and replacing them keeps the tub looking new.
Non-chlorine shock is gentler on surfaces but the dissolve-first rule still applies. The granules are sharp and can scratch acrylic if they sit on it.
Liquid sodium hypochlorite (chlorine) and liquid hydrogen peroxide are gentler because they need no dissolving. They are less common in UK retail but worth seeking out for show tubs.