I can say I've done it both ways with various guns, but always make sure it's pointed in a safe direction when connecting the air or adding nails/staples. I've never had one go off upon connecting the air supply to date or adding fasteners. I typically leave the fasteners in the gun until next use, but disconnect the air supply between uses. I even disconnect it when I'm in between assembly steps just because inevitably the cord gets caught and I drag the gun off the workbench.
Other than that, biggest safety, especially with brads is keeping your fingers out of the way by at least the length of the brad. Those thin ones have a tendency to follow the grain sometimes and poke out where you don't expect them, many times where you really want to hold the work at.
To a small child, the perfect granddad is unafraid of big dogs and fierce storms but absolutely terrified of the word “boo.” – Robert Brault