That depends...are you shooting black powder?
With BP, the case will shorten when fired the first time. If you full-length resize it you will recover most of the loss, but the case will never stretch enough to need trimming.
If you shoot brass (fireformed or resized) that is shorter than the chamber, you are likely to see leading in the throat. You can prevent that by fitting the case to the chamber, or by adjusting the bullet seating depth to leave a grease groove half exposed at the rim of the case mouth.
If you try paper patching with short brass, you will get paper rings left in the chamber.
CM