My father in law submitted his paperwork around January 15th. He picked up a gun on the 29th and the FFL said his DL indicated he had a valid LTC. So no background check was needed. I "guess" the license is happening when you get the e-mail confirmation and the rest of the process is waiting for the physical license to come in the mail? Not sure, but is it plausible. I would not assume this as you have to have the physical license to carry a gun. FYI.
My wife and I submitted all of our information (test, class, application, fingerprints, etc.) on January 12th, 2016. I hear it is taking 60+ days to get LTC licenses. Let the waiting begin!!