To get past the rough inspection, should I have the wiring for smoke detectors just pulled through the ceiling box (and stripped, pigtailed etc) or should I have the mounting bracket (for the detector) also installed?
The level of inspection depends on the inspector. Some get weird on a rough inspection with devices attached some love it. If your detector has a quick disconnect so it doesn't have to be unwired for the Sheetrock I would put it in. I regularly would wire outlets and switches that can be stuffed in the box when putting the Sheetrock up and the 2 main inspectors would ask if I wanted a cover or final because they had already verified my wire length & connection methods.
With this said I had 1 inspector that was a total nut case and went berserk with devices connected. After 3 hours on one occasion I called her boss she just had to find something. Only got her on finals after that. If the wiring needs to be disconnected to cover don't hook it up! Because this will be a waste of time.
Last but not least, four things they usually look at on rough inspection. #1 Make sure your wire lengths are 6" or more from the back of the box. #2 double gang or more boxes or a high wire count verify box fill. #3 make sure to correctly staple Romex flat and at proper intervals. Last all drilled holes 1-1/4 away from edge of board. These are the things I notice on rough inspection.
If the inspector fails you on any area ask for the code reference. I'm my state the inspector must cite the reference to write a violation. Whatever you do don't argue just take notes. That's the best advice I can give.