ok lets say it's been 2 days, if they go back to refill the supply they lose 4 days, no matter because they can refill, but since there back at the start they still have to travel the same amount of days to get the letter so yes they could, but it's kind of a waste of time.

EDIT: while I was doing the problem, you could have, for example, 3 people, and lets say it takes them 20 days, after 5 days, each person would have 15 boxes of food, one of the people could give 5 to one and 5 to the other and then go back to the base with 5 boxes to get back so it would work. I still don’t know the answer though -_-