It's just a funny thought as big mom seems to be obsessed with food. It's highly possible but Oda wouldn't let that come to picture. I highly doubt we will ever see any deaths of strawhats.
Luffy would never allow it to happen. He takes care of all his team members too much and he would stick by them
You might have noticed how persistent he is in this arc
i don't think so at all. she is obsessed with only sweets and not all the dishes. you could say that, sanji is good at all things and not just sweets. this is not possible.