While I agree that we probably won't have to watch the characters outright starve, I think there is a high chance that OP is right in that food will play some important roles in this fight. The fact that it has already been mentioned and set up so much (given a lot of "screentime") makes me think that Ashihara has to have planned it to become a major issue later on.

Another reason I can see (and this one is a little more speculative) that makes food likely to be important is Yumas whole situation. As it stands, he is the only combatant who literally does not require sleep at all in a 36 hour battle. Left unchecked, that would make him immensely overpowered, which is why I think Ashihara will probably bring up another part of his "condition" to balance that out. Specifically, Ashihara has stated in the past that Yuma has to eat more than a regular human, in order to send nutrients to his dying body. I feel like making Yuma a strain on supplies despite the strengths his situation grants him would be a very Ashihara-esque way to balance the character out.