Short answer is no. I do not think it is currently possible to dynamically change the label on that button. (Should, of course, be able to supply a custom translation to statically set the label, but it will not dynamically change based on context.)
I do have a couple of other thoughts. First, it is worth noting that there are some proposed UI changes that I believe would impact that button specifically (changing it to just a 
button following the standard material design). I am not sure how that might look different on a desktop browser, though.
Also, the idea of adding custom actions to the action bar is the kind of thing that would be really interesting to propose as a use-case for a plugin/add-on!