No effect at all.
Interestingly, in the settings, with all of the post menu hidden items selected to be hidden (including the edit button), the edit button still does appear (and all alone) but only on the Reply (non-Topic) posts.
So, with these settings…
This is what a Topic with one Reply Post looks like…
I actually appreciate that the Edit button cannot be hidden for Replies. Maybe a note should be made to reference that fact in the Settings, and the Edit button should be disabled from being disabled.