I think we would assume that it was in accord with Christ's will certainly but that is a side point, the question at hand is whether “prosopon”, often translated “person” at 2 Cor. 2:10, means something other than “presence”.
And to this question by what has been presented herein the answer is ‘No’, “presence” or “in front of” or “in the sight of” or “face” best sums up the meaning of “prosopon” and not something like “acting in the person of” or something similar.
Jesus was present when the Jews asked Him to be cruucified and Barrabas pardoned, so no, mere presence is not what is intended there. Besides, St. Paul asserted that he is acting in the person of Christ at other times as well:
be ye followers of me, as I also am of Christ (1 Cor. 4:16)