Only if there are no consequences.
Arguably, tracking hit points is just bookkeeping. If encounters never bring you to near death, than tracking hit points is just busywork.
If you're in a well civilized area then tracking food, ammunition, feed, and the like is unneeded. But if you're in a dungeon or the Underdark or the Isle of Dread or some ungodly swamp then tracking resources is basically hit points for the exploration pillar.
How much food determines how often the party might rest and if they travel that extra few hours or risk that extra encounter to avoid going hungry. How much water determines if the party might risk drinking from the forest pool or the underground spring. How much supplies determines if the party tries to parlay with the drow to trade for new stock or if they wait to see if they encounter less hostile races.
You can spawn some great stories and tension from tracking supplies. It's the difference between Voyager and Battlestar Galactica...