Yes and no, it depends on execution.
Search engines specifically state that paid links are against their terms of service. Meaning that if they discover a website has a paid link to another website, then they may remove the website in the PBN from its index. Sometimes, search engines may also apply manual actions on the websites receiving the backlink. This is normally the case where almost all the backlinks to the website are from paid sources, e.g. PBNs.
Generally speaking, if a search engine detects a PBN it will manually review the website. If the website does not pass the manual review, it will be de-indexed from the search engine’s results. This will result in the PBN having little to no impact on your SERPs.
If the PBN is executed to the highest of standards, then it will have a better chance of passing a manual review from a search engine and remaining in the index.