Looking at a profile shot of the Airbus, as opposed to the 737, I cannot see how there would be any effect of thrust over the tailplane; it's simply too high above the engine outlets.
Had a look on a take-off at the FLT CTL page as I rigidly held the half stick down position, and witnessed the full down elevator begin to rise at around 60 knots. Have not had a chance to look at the full stick down as yet; I now suspect it would retain the full elevator position all the way to 80kts.
Hence the fly-by-wire changes the relationship between the stick position and elevator authority as the airspeed changes even at these slow speeds.