The position of the control column depends entirely on the position of the actual control surfaces. So the answer to your question depends on how you interpret the question.
During "normal" flight, you would set your attitude, then, holding the control column (and therefore the control surfaces) in place, you would trim off the forces. So the control column would not move. Answer: No.
However, if you were to release the control column, and move the trim wheel (which is not a "normal" way of flying) then Yes, the control column would move.
Hope that answers the question. I dont' envy you rotary guys having to learn loads of pointless fixed-wing stuff to keep the examiners happy!
FFF
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