Should I Be Concerned With My Unit's Fatigue?

There is really no reason you should be worried about your unit becoming fatigued. Fatigue only takes effect after a battle ends, and unless you're currently such in a dungeon, all of your units will fully recover from it. If your units do become fatigued within a dungeon, you should have plenty of food to spare as offering anything, even a piece of bread, to a Mila Statue will fully heal the fatigue of everyone apart of the unit battling.