In a (D)SLR. When pressing the shutter release button the camera must first move the diaphragm to the required setting. When a small aperture is selected it has to move it more than when you shoot wide open. Does this affect the time between pressing the release and the opening of the curtain? Or do camera's always wait a certain amount of time irrespective of the aperture setting?
To help put things in perspective, the following vids shows (to quote a famous movie) "What a lovely ballet ensues, so full of form and color."
Nikon D3 11 FPS aperture and shutter acutation captured at 5000 FPS: http://www.youtube.com/watch?v=fG5QedhroYQ
Same thing, but with a D80: http://www.youtube.com/watch?v=qfruya5lNow
Want to see equipment from Canon? 5D, 5D Mark II, and 5D Mark III shutter only actuations: http://www.youtube.com/watch?v=RJ0GNzVUae4
Well, seing as the camera also has to swing a honking big mirror out of the way of the sensor before the picture can be taken, I think we can safely assume that it has plenty of time to stop down the aperture while it is doing this. Typical shutter response times for higher end models are on the order of 100 milliseconds, or 0.1 seconds, mostly because of the mirror. Unless it is a fixed pellicle-mirror camera (some new Sonys and a couple of old Canons) I cannot see how stopping down the aperture could possibly make any difference one way or the other.
Different manufacturers use different methods of stopping down the lens, so the time required can be highly variable from one brand to the next. Canon, for example, uses electronic communication between the body and lens and the diaphragm is actuated by a tiny servo motor attached directly to it. Nikon, on the other hand, uses a mechanical linkage between the body and lens. Since a servo directly attached to the diaphragm needs to move much less mass, it can be quicker while using less energy.
In most cases it makes no practical difference because the reflex mirror (The R in (D)SLR) takes much longer to move out of the way than the amount of time it takes to stop down the lens. Most cameras with mirror lock up will also stop down the lens at the same time the mirror is locked up. Taking still photos using Live View is the only scenario when any of my Canon bodies have to wait for the diaphragm to stop down. The delay is still less than when using the viewfinder and waiting for the mirror to move.
Since most current DSLRs can shoot several frames per second even when moving the mirror up and back down and refocusing between each shot, the amount of time needed to stop a lens down to any aperture is fairly negligible.