No, it should be delayed. That's why I like a rations-like approach. The basic gameplay idea is to provide an incentive to looting.
So, one idea would be to have a "rations" attribute for units. It would count in days, and would automatically be scaled to unit size. So yes, if soldiers die,. their rations would be lost. Not 100% realistic, but simple and predictable. And it saves us from trouble such as calculating what the effect is when 10 soldiers of an 80 strong unit die (i.e. fractions of days).
Rations would be slowly replenished in certain areas (food supply, barracks, or something), but could also be quickly replenished by looting.
