I'm talking, how much time can be expected to elapse between the user touching the screen and something like touchesBegan being called? (Or something lower level, if such a thing is available.) Sub-millisecond? Multiple milliseconds? Tens?
I'm pretty sure touchesBegan is called very quickly (meaning, with whatever minimal delay exists in the event path). I've noticed in my code that I get a single touchesBegan for a two-fingered touch with both touches already in the list. I assume that I don't touch both fingers down together very precisely but from what I've seen the touchesBegan event is delivered within a few milliseconds. I suspect Apple holds the touches very briefly before passing them along in order to batch them for more efficient handling, possibly also using that delay to filter out accidental touches (sort of like de-bouncing a mechanical switch).
I use a touchesBegan in my view to freeze my scrolling animations and my perception is that the scrolling stops immediately when I touch the screen.
The real delays come from the gesture recognizers. They often have to wait to see if you've moved far enough to signify a pan or if you've held long enough to be holding or if you've released without dragging to signify a tap. Those delays can be substantial of course, though they're still only a fraction of a second in my experience.