I think changing avatar does line up a rebake of the user’s quoted posts? I’m not sure on the schedule though.
Edit: I am now not sure. 
I have been waiting patiently for it to magically kick in on my test site, but no joy yet. I could have sworn I’d seen it in action on a forum I’m not a staff member of, but looking back over a few oneboxed and quoted links from there over the last month it appears I still have an older avatar in those. 
When I searched I found this, which I thought confirmed that it did line up a rebake for them, but I think I may have got confused: