Impossible to predict what impact it will have between her and OM but, as you say, either way doesn't really matter since it doesn't change what you need to do
Me, WW - Upper 30s BD - Apr 1 2016 EA - Apr 7 2016 (discovered; ongoing for months; did not confront right away) Confronted wife about EA - May 17 Wife sent NC email to OM - July 11