Yes. Network-activate it and every site is set up, including sites added later: as many as it can in about three seconds, and each of the others the first time WordPress runs on it. Each keeps its own settings, its own record and its own visitors' answers. On a network set up with sub-directories (example.com/shop/), where every site shares one address, each site keeps its answer in a cookie named for that site, and so does WP Consent API if you have it, so an answer given on one site does not count on another; visitors who answered there before this was so are asked once more on each site. After the update the plugin empties every site's page cache, starting the first time anybody opens wp-admin on the network or at the next daily check and going on, about three seconds at a time, with each wp-admin screen or daily check after that until every site is done, as far as the caches switched on for the whole network go; a cache switched on for one site only is emptied when that site's own wp-admin is opened or at its own next daily check, and a cache the plugin cannot empty serves pages from before until they expire. A site whose translations are in language folders keeps one answer for all its languages; a visitor still holding the separate copies 1.3.2 kept for each language folder has them folded into one, the answer given last, the first time they open a page in that folder. A network set up with sub-domains keeps the cookie it always had.
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