Boeing in their class manual,
Jet Transport Performance Methods, page 17-15,
It’s worth mentioning here that the VMCG constraints shown above do not include consideration of a crosswind. However, a crosswind from the direction of the failed engine would significantly increase the minimum control speed. In the illustration above, a crosswind from the right would be adverse, because it would cause the airplane to “weathervane” – that is, turn its nose toward the direction from which the wind is coming. A crosswind coming from the side opposite the engine failure would be favorable.
Yes, but think of how an upwind engine loss would affect your yaw moments. If you are applying downwind rudder to counteract the weathervaning in the crosswind, you’ll have less rudder to counter the engine swing. FAR 25 used to use a 7 knot crosswind, then dropped it as a certification standard.
Yes, no one accounts for crosswind effect on Vmcg, but it’s there even if it would be a real bad day that you had a strong crosswind and an upwind engine loss near Vmcg. But, any take-off scheduled where V1 is limited by Vmcg should be pause for thought.
GF