I think this primarily depends on whether the edit improves the post or not.
When one simply replaces a working link to some post with their own share-link to the same post, this is definitely uncool, primarily because such an edit is useless from readers perspective. But as you ask about posts that don't "have the relevant link in it", it's not your case.
When the edit inserts links to posts instead of forum/chat like garbage like "as mentioned by @username", it's a real improvement as it makes it easier for readers to follow the referenced post.
In cases like this, using "own share link" is OK because, well, that's what is shown to the editor under the posts they link to. They sure have a right to "de-personalize" that link by manual removal of their id from the URL if they want, but if they prefer not to mess like that, I believe this is totally OK.
For adding links to questions it may feel a bit more complicated but it really isn't.
As opposed to answers, questions offer editor an option to pick between the de-personalized link at the title, like
http://meta.stackexchange.com/questions/197743/own-share-links-when-editing-other-peoples-posts-in-order-to-increase-badge-pwn and own link at share, like
But thing to keep in mind here is the same as when adding links to answers. As long as edit improves things for readers of the post, it doesn't really matter which of two links were picked. And, conversely, edit that is useless to readers (eg adding link to irrelevant question) would be "uncool" even if editor would use de-personalized link.