According to what I have read in the Scriptures, conceit, which is the idea of the personal identity, doesn't fade away until one's fully enlightened. So I would assume that the wish to become still exists until conceit has totally been eliminated. This is the case because a partially enlightened person, at the level of a stream-enterer still has sense desire and aversion. Even a once returner has sense desire and aversion. The non-returner apparently has eliminated all sense desire and aversion but they haven't eliminated fear and worry which is, from my understanding, all about the future and so there is still this projection of a self into the future. So they have concern about fear and worry, so I would believe there would still be becoming in that.