multi buffer: completed job return guarantees

Given a multi buffer manager with a runtime parallelism of `n` (i.e. it can work on `n` buffers in parallel), is it guaranteed that submitting `n` jobs will return at least one? Or does one need to submit at least `n+1` jobs in the worst case (empty manager)?

It seems to me that submitting `n` jobs is enough to get a completed job back even if the manager is empty; but I would like to get confirmation that this is indeed guaranteed.