Save the first edit of an [on-hold] question for fixing the issue of the question (or working towards it)
As you implied in the question, after being put on hold, the first edit to the question will kick it into the queue to be reopened. This mechanic is there to make question fixes more visible and to help get those fixed question reopened.
However, if you make an edit to the question as the first edit that does not work towards fixing the question's closure issue, you are making it more difficult for that question to be reopened later. So, if you have an edit that doesn't help the question get reopened, save it until after either that first edit is made or the question gets reopened. After the first edit is made, there is generally no harm in making edits as usual.
Editing a question after it has been [on-hold] for 5 days and been moved to [closed] apparently does not move it into the review queue.
It is worth noting that making cosmetic changes to on-hold/closed questions that may not get reopened is not usually advantageous. If that question never gets fixed and reopened, that cosmetic change doesn't really matter and could be wasted effort. It is also possible that the question could go through drastic changes and the stuff you prettied-up might get removed or overwritten entirely, also becoming wasted effort.