(a) No. There are many different situations in which, because of the relationship of the parties, or because of the particular circumstances, it will be inferred that there was no intention to be legally bound. This includes, for example, when agreements take place in non-commercial contexts, such as between friends, or to provide volunteer or charitable services. Such agreements will not be treated as intended to be legally binding unless the person who wants to enforce the agreement can prove facts from which an intention to be legally bound can reasonably be inferred.
The present example involves volunteer services and there are no additional facts from which it can be inferred that the agreement was intended to be legally binding. It is therefore unlikely that a court would enforce it.