This answer was superseded by an update as outlined in the answer here.
(Note, this is the same as my answer to the duplicate question I asked: Why shouldn't I edit a question that has been closed?)
Editing closed questions puts them back in the review queue, and if the edit was unrelated to the close reason, the question will be kept closed
Firstly, I will point out that I've done exactly the thing I ask about in the question, and it was V2Blast♦ who pointed out to me why I shouldn't do this. I've since abstained from doing this, but I've seen some users still do this; I just want to point out that I learned the hard way, and that's why I now know this.
If you edit a closed question, that triggers the question being put into the Reopen review queue. The intention behind this automatic behaviour is that, if a closed question is edited, the hope is that the edit is an attempt to rework the question into a "stackable" state. The reviews will consider the edit to see if it brings the question in line with the stack's expectations and votes to Reopon or Leave Closed accordingly (or make further edits, etc).
However, if the edits were of a trivial nature (by which I mean, not specifically related to the reason the question was closed), then when it gets put into the Reopen review queue, the actual content and question(s) remains the same, just with better tags or corrected spelling. In other words, the question now being reviewed is essentially the same question that was originally closed, so the reviewers will just vote to Leave Closed, since nothing significant has been changed.
Why is this a problem?
The problem with this is that "everybody gets one". Once the question has been through the Reopen review queue, that's it. It doesn't get another shot at it. If further edits are made later, it doesn't get put back into the Reopen review queue, so it will only be reopened if people happen to manually check back and take a look at the question, unrelated to the review queue.
Hence trivial edits can actually potentially prevent the question from being reopened if the OP does later edit the question into shape, because the question has already gone through the Reopen review queue due to the trivial edits.
Hold off on trivial edits until the OP has edited their question with relevant improvements
Once the question has been edited by the OP to include the information needed to consider reopening it (meaning, gets put into the Reopen review queue), then you can make more edits on top of that, because it would now be put into the review queue for the right reasons, and further "clean up" edits won't interrupt that process.