Hi ndg

Yes it is true and also tested.

Vmc is the calibrated airspeed at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with that engine still inoperative and then maintain straight flight at the same speed with an angle of bank of not more than 5 degrees.

When weight goes up the aircraft will have to fly at a higher Angle Of Attack (AOA) to produce the extra lift needed. Increase in AOA also means an increase in P-factor which is the reason Vmc is increased.

Propellers have what's called "P-factor" when the airflow into them is not parallel to the propshaft, such as when the airplane is at a high angle of attack during climb. The skewed airflow relative to the prop disk causes the blades on one side of the disk (the downward-moving blades in the case of a nose-up climb) to see a higher angle of attack and airspeed than the blades on the other side. This causes them to make more thrust than the blades on the other half of the disk. The unequal thrust tries to yaw the plane towards the side of the disk that has less thrust, typically to the left for one of the right-handed props we typically use in the USA.