I cannot speak for all Banks policies, but that isn't how the 'overdraft protection' on my account works. How mine (actually a credit union, maybe thats a difference) works is:

Without it, if I was to write a check with insufficient funds, I would get charged some large fee. But with the Overdraft Protection, it will transfer money from my savings account to checking to cover it, for free, helping me avoid the fee. Essentially it lets me use the savings accounts as a safety net to avoid the charges.

This 'protection' has in fact saved me in a couple of instances.