NO! They do not.
When you apply for a new bank account, they do not run an inquiry on your Credit Reports. They do not use them as a decision.
An inquiry that will appear on your ChexSystems Report. You do not want to keep going from one bank to another trying to open up account if you continue to get declined. This will result in multiple inquiries on your ChexSystems report.
Your credit does not affect the decision whether or not you will get a bank account.