Viscosity Index does matter to diesel but it's not used as widely as it's cousins, pour point and cloud point, that describe the highest temperatures of solidification.
Viscosity index is used to describe the flatness of the viscosity (ability to or resistance to flow) over temperature. Since lubricant oil is a complex blend, the property varies a lot.
Diesel is almost purely C12 - C18 and it is the amount of higher number waxes left behind that matter, not viscosity itself. When it turns to a waxy gel, it cannot be injected into cylinders.