According to the website of  one of the Big 5  (not the bank in question, though) this is what would happen:

"11. What happens if I try to make a purchase with my credit card and exceed my credit limit?

If you attempt to make a purchase that exceeds your credit limit, your purchase MAY be declined. If a purchase is approved, by allowing you to exceed your credit limit, you will be charged a $29.00 overlimit fee. "