I'm pretty sure the credit check is done automatically by the dealership software, as part of entering a person into the system to get their paperwork filled out. It's probably done to save time because 99.9% of the time it's necessary. The credit check won't stop the sale if you're paying with a briefcase full of cash or writing a check.

That said, going in with a briefcase full of cash is going to cause a lot of other problems.