Having worked at a consumer bank for a considerable amount of time and being someone quite familiar with credit requirements and underwriting, I can say that having a banking relationship at the bank you're applying for can help or even hurt you in the application process. Here's why...

1) Opening an account for the sole purpose of "having a relationship" could actually lower your score. Why? Some (most) major commercial banks do a credit inquiry when opening accounts for consumers. This is used to mitigate risk and also track collections and judgements. It is also used to establish pre-approvals for both secured and unsecured credit cards for new/existing customers.

2) If you already have an account somewhere and have ever had a charge off or are a regular overdraft offender, the bank can use your relationship history against you when deciding on credit offerings and even terms if/when approved.

3) If your credit is less than perfect (think 620 or less), a bank might overlook you for an unsecured credit card and offer you a partially secured or even a fully secured card -- especially when they already know what kind of balances you carry in your deposit accounts. That way, they know they can collateralize your credit card and they know if you can afford it.

4) If you've ever had credit products with the bank your relationship is at, there is a higher chance of them using your payment history with them against you when granting you revolving credit (a credit card). If you've had delinquency of mortgages, have done a loan modification, or ever declared Ch. 11, you're likely SOL.

But alas, there is hope (for some). If you have stronger deposit balances in your accounts or have investments/CDs/IRAs with considerable balances, many banks will overlook credit issues when granting revolving credit so as to ensure that they don't jeopardize your deposit relationship and alienate you as a customer. Or, if credit analysts deny your initial credit application, account managers (preferred/premier/private banking) usually have leverage to negotiate with the credit analysts and grant you credit, regardless of FICO score.

Hope that helps!