How long? That, sirrah, depends entirely of the CLEO. Some may complete the paperwork the day recd. Some will not have completed it when Hell freezes over. Why? As many different reasons as there are CLEOs. Why would they turn you down? Don't believe anyone should have a Class III, your Uncle Timmy was a no good drunk, and you probably are too. There is a lot of drug dealing going on out where you live in West Tree Stump, and I don't want any full autos that may end in in a meth lab. Their wife would not.... well, anyway, you get the idea.
There IS a legal way around the CLEO that will approve NO class III papers- get a lawyer (notice I did NOT say use Legal Zoom or any other computer software, I said GET A LAWYER) and establish a legal trust that will own the Class III. Now, no CLEO approval is required. Nor prints.