Should questions with such content be edited?
If you are just editing the post to remove the
http://www part from the links that don't take to any real page, or to change the domain name to example.com, then I would say you should avoid editing those posts. If there is something else to edit, and you also change the domain name to example.com, then I would say the edit is acceptable.
I would not worry about links taking to not existing pages, if not in one case. Suppose that a question is about something noticed in a web site for which the OP provides the link, such as the following question:
I want to implement the image carousel used on http://domain-name.com/page.html. How do I do it?
If the question doesn't have any screenshot that shows the type of image carousel seen in that website, and the link returns an error, then the question could be closed as too localized. I would not bother editing the link, in such case.
As side note, there is already a mechanism to warn users about wrong links, which checks the domain name. Try using
http://www (without closing it between back ticks), and you will get the following error message.