Yes he would have lowered the hammer on a live round, it is safe to do on all modern revolvers, unless he was carrying and old Colt Single Action Army revolver which was unsafe to carry w/ 6 rounds loaded. S&W Model 29, the gun he carried in the film, has what's called a transfer bar. Unless the trigger is pulled -and held- the gun will fire. If the user holds the hammer with the thumb, releases the trigger once the hammer is free to move and lowers the hammer the transfer bar prevents the firing pin from striking the bullet's primer. You can bang the hammer with a rock and that gun will not fire. Otherwise what is he going to do with the gun, you can't carry a revolver cocked. That's called single action and the trigger pull is VERY light. There are two things that would have happened in real life. One he wouldn't have carried that gun. Only Detroit authorized police to carry and issue 44 magnums. SFPD would have issued him a 38 special, police officers can't use whatever gun or caliber they want. Second he'd never be able to cock his gun. Police revolvers were Double Action only, meaning you can't cock it. Cocked, or single action, makes it far too easy for a gun to go off under stress. In the movie Harry only fired 5 times, he lowered the hammer on the 6th so when he turned around and cocked the gun again the cylender rotated past the live 6th round and he dry fired on the first spent shell fired.