Yes. On day one they give you a QR code that links to a form to request the base and check airman you hope to do UOE with. They try to accommodate. So even though I was based in PHX when I upgraded I was able to do UOE at my home in DAL. It’s Lead Ops though so YMMV.

(Edit: wait, now I see you were suggesting that he could get his UOE done quicker if he is willing to go to another base. My bad.)