Hoo boy, you have said the "G-P" words.
Whether it is really precession, or whether G-P is a simple way of explaining the delay between the point when one blade gets a boost (or loss) in lift, and the point where it has reached its maximum movement (up or down) as a result of it, the answer is this:
It happens any time there is a difference in lift between the blades.
It might come from the first moment of moving forward (resulting in flapjack) or when the change in inflow as a result of rotor tilt (inflow roll) but it is still the same stuff.
The first one that happens is flapjack, even from a 1-knot difference in relative wind onto the blade. Inflow roll happens a bit later.
And by the way, "G-P" also "happens" when you move the controls to tilt the disc, and the swash plate uses its advance angle to make up for phase lag.