The short answer
Probably yes — “sharing” covers ordinary ad pixels, so most stores owe an opt-out that actually propagates.
California does not run an “Accept cookies” wall. It asks for notice at collection, a working “Do Not Sell or Share My Personal Information” mechanism, and automatic honouring of the Global Privacy Control signal. The regulations are explicit that a cookie control is not by itself an acceptable opt-out method, which is why UserGuard ships Do Not Sell as its own mechanism with its own link, panel and record.
What a browser-side opt-out can reach, it reaches: it gates the tags on your pages and publishes the USP string vendors read. What it cannot reach — server-to-server conversion APIs, CRM syncs, audience uploads, data you sell directly — stays yours to switch off. Pretending otherwise is the exact failure mode behind California’s largest settlements.