When you say "free of all Dukkha", yes, that's actually a wish that one day the person becomes enlightened. Either as a Buddha or an Arahant.
And yes, I would love not only to become enlightened, but I'd love to help people along the way, too, which is kind of what I do. Having that joy not only for oneself to become enlightened, but also in helping others, is certainly a very big one.