Not a common use of the term 'critical engine' in respect of crosswind handling considerations. It is usual to consider the certification meaning.
So far as the crosswind concern might be a worry, consider the following situation when it is a REAL worry. Try a min V1 takeoff, strong crosswind from the side with the V1 failure, and aft limiting CG ... it is called .. running off the side of the runway ..and is pretty well guaranteed.
Always gets the students' undivided attention when you give them the exercise in the sim on endorsement training and helps to keep the consideration in the back of their minds for line ops.