The initial distribution of property is not very important for an-caps. Most of the value is not in raw resources but in what is made from these resources. Some an-caps believe in equal distribution of resources (i.e. georgism), but most believe in the homesteading principle which says that the first person who puts the resource into use owns it.
And no. They do not have the right to let others starve. There is nothing that can be done with a coconut surplus that justifies your argument. They cannot invest it. They cannot give more in other ways. It is hoarding, pure and simple.
Why do you blame specifically people who hoard coconuts for this though? What if a week ago you couldn't even get all the coconuts, but it is because of the ingenious methods developed by these entrepreneurs that it became possible? In that case you cannot blame them for something that was not even available without them. But even if you disregard this, why blame them and not the rest of the population? Those entrepreneurs are not the only people who gather food. Surely there are some fishers, or hunters and such, or people who gather other types of fruits.
Now we both know that people do not hoard resources (maybe unless they themselves fear from future starvation), it is silly. No one does that. Instead people trade resources. So it is extremely unlikely that those entrepreneurs would hoard the coconuts, they would just trade them. So I ask you again, would taking some of the surplus by force by justified for taking care of the sick?