To add a bit to Dave's answer...
There are also another couple of factors that are airbrush dependent. The length of the paint channel between the color cup and the nozzle can also play a factor when spraying, depending on the consistency of the paint, and whether or not there is already enough paint in the channel to send out. For example, gravity feed cups usually have a slightly faster paint flow response than side feed, or siphon feed airbrushes, as thanks to our friend gravity, there will almost certainly always be paint already in the paint channel around the needle. If there is enough time between strokes in a siphon feed, gravity will tend to pull the paint back down into your bottle, and you might need just a fraction of a second more to get paint flowing.
So along with air velocity coming out the front, the length of the paint channel and the type of airbrush can also play a role. In regular use however this is usually just a tiny fraction of a second, and often something you might not notice. If you switch back and forth between brushes in the same session, or are experience, especially in detail work, you may notice the difference and come to adjust your pressure, or style to compensate when starting or stopping lines.
With siphon or side feed, as long as you keep paint in the channel all the way to the tip (don't wait a long time between lines), well... the start time should be as fast as any gravity feed.
Almost all that a regular user will notice tho, is the the amount of air pressure will definitely effect paint flow speed, due to the reasons in Dave's excellent explanation.