Is such behavior considered correct?
No, it isn't; it's utterly unacceptable. If you see behaviour like this, flag the user for moderation attention (they're not likely to stop if you leave a comment). The Help Center clearly states when it's appropriate to make an edit:
Tiny, trivial edits are discouraged - try to make the post significantly better when you edit, correcting all problems that you observe.
Editing a post also bumps the question to the top of the homepage. Please be mindful of this and make your edits count, so that the new attention is brought to something substantial.
As Catija outlined, cases where the pronouns of the author are important enough to be included in the question are few and far between, and they mostly happen on social sites in the network. Certainly not in random feature requests on Meta Stack Exchange. They're noise and have no place in posts like that. Moreover, 99.9% of the users[citation not needed] associate the name 'Tim' with a male person so the information is completely superfluous. The correct place for that information is the user profile, as stated in the FAQ:
Q8: How should I identify my pronouns if I choose to do so?
Whether and how you identify your pronouns is up to you. If you choose to do so, add it to the “About Me” section of your user profile.
As the user admitted here and here,
they're ahem ... he is just looking for a soapbox and is completely aware that his behaviour is disruptive. There are enough posts on Meta Stack Exchange to vent his opinion, and he could also use his profile page for this. If this would happen on one of the sites I moderate, I'd suspend him to cool down. I can't do this here, and my custom flag raised yesterday evening asking to do something about the situation is still pending, so all I can do now is rollback the edits.
My pr ... no, this subject is too delicate to even make that kind of jokes.