Does transactional work when calling public method from private method?

I have method like:

private fun exchange(entity: Entity) = 
    subAccountRepository.save(entity)

This method calls repository:

@Repository
interface SubAccountRepository : R2dbcRepository<SubAccount, Long> {
}

Save responds to public method in Spring:

@NoRepositoryBean
public interface ReactiveCrudRepository<T, ID> extends Repository<T, ID> {
    <S extends T> Mono<S> save(S entity);

And the default implementation in Spring is:

@Transactional
public <S extends T> Mono<S> save(S objectToSave) {
    Assert.notNull(objectToSave, "Object to save must not be null!");
    return this.entity.isNew(objectToSave) ? this.entityOperations.insert(objectToSave) : this.entityOperations.update(objectToSave);
}

Does @Transactional work that way - when called from private method in code ?