On an A320, will the aircraft compensate for constant pilot rudder input?
Will the aircraft compensate for constant pilot rudder input? No.
It seems you're asking if a pilot can deliberately sideslip an A320 while in normal law (Gimli Glider style).
The answer is yes. The normal law won't fight back.
The question has been asked years ago on pprune.org, where one person replied:

Great question....one that is misunderstood by many....too many.
Please refer to FCOM 3.04.27 P4, FCTM NO-160 P 3/12 (24 JUN 09), and Airbus Flight Operations Briefing Note &quot;Landing Techniques....Crosswind Landings&quot; (April of 2006).

The user is referring to the pilot being able to indeed induce it during a crosswind landing before touchdown (unlike pitch, there is no flare mode for roll/yaw).
But if you're like me, you'd want more proof. Sadly the proof comes from a 2012 incident where the captain was incapacitated and involuntarily pushed on the rudder pedal:

(Final report)
The relevant text from the final report reads:

Approximately seven seconds after the captain’s last attempt to communicate, autopilot 1 was disengaged by the co-pilot, at this time the travel of the captain’s right rudder pedal reached approximately 13 degrees, and the Aircraft started to sideslip. The co-pilot disengaged autopilot 1 when he decided to take over control after realizing that the Aircraft was side-slipping. However, after the autopilot disengagement, the captain’s right pedal was still being subject to pressure continuously while it maintained a position of 14±1 degrees for another 18 seconds.
Autopilot 2 was engaged by the co-pilot in order to reduce the workload, but after seven seconds, the co-pilot disengaged it due to, most probably, noticing the continuous input of the captain’s right rudder pedal, which put the Aircraft into a 10 degree sideslip, and to lateral acceleration that reached approximately 0.26 g.
After the 18 second period of constant pressure on the right rudder pedal, the rudder input started to decrease and the pedal returned to the neutral position within 11 seconds. During the 29 seconds from the captain's full coma until the pedals returned to the neutral position, the co-pilot was making continuous attempts to recover the Aircraft to straight and level flight manually.


Addendum: Note that the A320 normal law doesn't aim for zero sideslip, rather coordinated turns, i.e., when a roll is commanded with no pedal input. Also a pre-programmed partial rudder input is made when an engine fails, but the remaining required input is left to the pilot (to maintain the pilot's instinctive reaction). And finally yaw damping acts on the yaw-rate (oscillation) due to Dutch roll. None of which would (nor should) act against a pedal action (as the incident and crosswind landing technique demonstrate).
In yaw damping and turn coordination, the one-way artificial feel cancels any feedback on the pedals (and adds feedback when yaw trim is input), but a pedal action will always work the opposite way on the rudder.