When a question is locked, the "edit" link is inactive. I think that the "edit tag" link should be inactive, too.
From what I have tried on math.SE, it seems that when a question is locked, you can click on "edit tags" but when you try to save your edits, you get an error saying: This question cannot be edited at this time.
I was not able to see the same behavior here on meta.SO, probably because I do not have sufficient rep to edit posts.
You can see an example in this post on meta.math.SE. (I will post also some screenshots here.)
I tried to find out whether this has already been reported here, I only found this question: The new AJAX tag editing works for locked questions. It is not exactly the same and it is marked as status-completed.
Here are some screenshots: