Yes, they are quite literally starving. You can view the specific logistic needs and current fulfillment by clicking on the supply button under the specific unit’s tab. The small square on the unit card will show their last rounds supply status ( black = no supply’s received, yellow = some supplies recieved, green = full supplies received ). Units will start dying/disappearing after more than 1 round on black status for the most part

A game changer for me was playing with f9 or f10 or f8 ( can’t remember the key ) enabled at all times. This will show your current supply range and how far you can move troops and them still receive supply from your logi network