I've sometimes seen questions that are on hold, where the topic interests me and I think I can get one in under the wire. Is it unfriendly to the O.P. to write a new question immediately?
Yes, it is unfriendly.
Questions are on hold pending improvement. You have recognised that there is the kernel of a good question. If you can improve a question without destroying it completely you should suggest a revision (that is, edit it; edits from users with less than 2000 rep are reviewed rather than accepted immediately).
Once the question is edited, it goes into a queue for review and potential re-opening. If it's reopened, you can answer it.
This is exactly the same method as for a question which isn't "on hold" — if the question can be improved, improve it. And, indeed, it's the same for a question which has moved from "on hold" to "closed": if it can be improved and re-opened, improve it.
If a question has been closed because it wasn't improved, and it's unlikely that it could be edited to be better, then by all means ask a better question.
Quite what would happen if you were unfriendly and pre-empted the holding pattern, I'm not sure. You could find that the original question is edited to be better and reopened, and then your question is marked as a duplicate.
By default yes I think this is an unfriendly thing to do. However there are two relatively common factors that can turn things around.
Before we look at those, let's note that the goal of asking a question should never be to "get one in under the wire". We're not just trying to get by. The goal should always be the most constructive well scoped expert level questions on the internet. Obviously everything is going to miss that mark, but lets not forget that that is the mark. Lets not aim for passable.
Now, should you ask another question?
Are you actually asking the same thing?
If you are really looking for the "same info", then probably not. The best thing to do is not snipe the topic with a new question but fix the existing one. If you can think of a way to make the question constructive, edit away. On closed questions it is not nearly so critical that you preserve the authors original intent. Common courtesy says you should try, but sometimes their intent will be outside the scope of this site and their choices will be between their pet question staying closed and a modified question that can actually contribute to the site. The author can always rollback and other community editors can even try taking it different directions until one finds a way to get it re-opened. Once the question is opened, major changes of direction should be minimized again.
On the other hand if you are actually looking for something a bit different that might stand up as a unique question because it has its own scope and focus even though the overall topic might be related, it is perfectly acceptable to ask another question. In this case it is usually useful to throw up a cross-linking set of comments on each of the related posts. The original questioners might be interested in the other question and anybody answering might be interested in addressing one or both questions keeping in mind the specific scope.
Is the author of the original question playing along?
Again, if they are willing to work with us to make their question appropriate for the site it is best to help them get their question opened.
Unfortunately some of the time nonconstructive questions come from nonconstructive attitudes. If constructive feedback has been given and refused* on the original question — or there is sigificant indication that the question is asked in bad-faith — then it might be time for somebody else to ask the same question in good-faith.
* No reply to comments is generally not the same as a refusal. That usually means the question is fair game for editing. An edit reversal or an explicit comment would count as a refusal.