Hi CONF iture,
It certainly won't efficiently as the elevators are commanded nose-down as a start....
Instantaneous ?
It does not have to be, what matters is the intention, the intention to efficiently deliver.
Please have a look at
Airbus A320 Fly By Wire Demo - YouTube from time 12:00. (link posted by alonso1986 in another thread)
There is an AoA gauge fitted and visible to the bottom left of the PFD.
During the demonstrated pull up manoeuvre, the AoA increases rapidly to 15 degs during the +ve delta g. During the steady 1 g climb, as the speed washes off, the AoA increases towards 15 degs again steadily over about 10 seconds. The AoA never exceeds its design limit (apparently 15 degs mentioned around time 10:00).
That is the sort of manoeuvre the system was designed for, and performs it very well.