Sure they can, and most likely will…
Unpaid parking tickets in themselves do not appear on your credit report. However, in most cases they eventually go on your credit report as collection accounts or public records (judgments and liens). Both are equally bad for your credit.
When parking tickets go unpaid they are either sold to a collection agency (which reports them to the credit bureaus) or result in a law suit. Many of these lawsuits end up in a judgment against you. In the end – not only you’ve ruined your credit, but you’ve also accumulated interest, fines, legal fees etc.
When these go unpaid – the court can garnish your wages or bank account or put a lien on your vehicle. All of this is really bad stuff for your credit.
My advice – pay these tickets. In the end it’s the cheapest option!