Does the auto thrust at takeoff compensate for asymmetric engine characteristics?
@JuanJimenez's comments are correct. N1 (and the accuracy of EPR) are not indicators of a precise thrust force.

So to answer the title question, generally no, moreover the acceleration of each engine may be different, and that is why the pilots go through a stabilization step, where they apply some thrust, make sure they're responding in a sufficiently similar manner, then they proceed with takeoff thrust. The pilots will correct any yaw with the rudder, and any remaining effect could be similar to a very light crosswind.

Also see: How is thrust of engines on the two sides of an airplane kept exactly equal to prevent yawing? The same phenomenon due to wear and tear is discussed. It is trivial for the most part since there is a rudder.

Of course this affects fuel consumption in-flight as there will be a tiny yaw as well that needs to be trimmed out.

But don't take it from me, check the Airbus article, Engine Thrust Management - Thrust Setting at Takeoff.


  Every engine has its own performance level due to manufacturing tolerances. In addition, engine performance evolves with time due to wear and ageing. As a consequence, the acceleration profiles may slightly differ from one engine to another on an aircraft (fig.3), even if fitted with new engines.
  
  Similarly, the idle thrust can slightly differ from one engine to the other, moving the acceleration profile to the left on the graph (fig.4).


Earlier I said generally no, because there are always exceptions (never say never on the internet). The articles notes that the Trent engines of the A330 and A380 automatically manage the stabilization step.




RE notice: On old aircraft before FADEC pilots were manually adjusting the thrusts to be equal (...)


It's because before FADEC the link between each lever and engine was a cable, and each cable depending on its age and environmental factors, acted differently – different stretching, friction, set torque, etc.

With FADEC, this is no longer a problem. The same electronic command is sent. And depending on the target, e.g., x N1, this is what the engines aim for, regardless of each engine's age and the fact that exact N1 values don't mean the same thrust force. Pilots pre-FADEC, like pilots with FADEC, don't know the thrust that is being applied in lbf/kN.